Finite Group Databasebeta

← Group #10826285

Character table — Group #10826285

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888121212121212121224242424242424244848
order1222222222223444466666662244444444666666661212121212121212121212121212121244444444121212121212121212121212121212121212888888884444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ4111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-111-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-11-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-11-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ1211111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ1311111111-1-1-1-1111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ1411111111-1-1-1-1111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ1511111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-11
χ172222222222222-2-2-2-222222222222-2-20000222222222222-2-2-2-200000000-200-20000-2-20000-2-2-2-200000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-200002222-2-2-2-2-2-2-2-2-2-2-2-20000000020020000220000-2-22200000000000000000000000000
χ19222222222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ20222222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111112-2-22-2-2-2-2-1-11111-1-1-1-111111111000000000000000000
χ21222222222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2111111-1-111-1-1-1-11111000000000000000000
χ22222222222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-111111111-222-2-2-22211-1-1-1-1-1-1111111-1-1-1-1000000000000000000
χ23222222222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-20000-1-1-1-1-1-1-1-1-1-1-1-11111−i3−i3−i3−i3i3i3i3i3-200-2000011−i3−i3i3i31111−i3−i3i3i3−i3−i3i3i3000000000000000000
χ24222222222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-20000-1-1-1-1-1-1-1-1-1-1-1-11111i3i3i3i3−i3−i3−i3−i3-200-2000011i3i3−i3−i31111i3i3−i3−i3i3i3−i3−i3000000000000000000
χ25222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-20000-1-1-1-1111111111111−i3−i3−i3−i3i3i3i3i320020000-1-1i3i3−i3−i311-1-1−i3−i3i3i3i3i3−i3−i3000000000000000000
χ26222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-20000-1-1-1-1111111111111i3i3i3i3−i3−i3−i3−i320020000-1-1−i3−i3i3i311-1-1i3i3−i3−i3−i3−i3i3i3000000000000000000
χ2722222222-2-2-2-22-2-2-2-2222222222-2-2220000-2-2-2-22222-2-2-2-2-2-2-2-200000000200-2000022000022-2-200000000000000000000000000
χ2822222222-2-2-2-22-2-2-2-22222222-2-222220000-2-2-2-2-2-2-2-22222-2-2-2-200000000-20020000-2-20000222200000000000000000000000000
χ2922222222-2-2-2-2-12222-1-1-1-1-1-1-122-2-2-2-222221111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-2-2-22-2-22211111111-1-11111-1-1-1-1000000000000000000
χ3022222222-2-2-2-2-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-21111-1-1-1-11111-1-1-1-111111111-222222-2-211-1-1-1-111-1-1-1-1-1-11111000000000000000000
χ3122222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-222-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-2-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000
χ3222222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-222-2-2-2-2-2-211111111-1-1-1-1-1-1-1-1111111112-2-2-22222-1-111111111-1-1-1-1-1-1-1-1000000000000000000
χ3322222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122-2-22200001111-1-1-1-111111111−i3−i3−i3−i3i3i3i3i3200-20000-1-1i3i3−i3−i3-1-111i3i3−i3−i3−i3−i3i3i3000000000000000000
χ3422222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122-2-22200001111-1-1-1-111111111i3i3i3i3−i3−i3−i3−i3200-20000-1-1−i3−i3i3i3-1-111−i3−i3i3i3i3i3−i3−i3000000000000000000
χ3522222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-2-22222000011111111-1-1-1-11111−i3−i3−i3−i3i3i3i3i3-2002000011−i3−i3i3i3-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000
χ3622222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-2-22222000011111111-1-1-1-11111i3i3i3i3−i3−i3−i3−i3-2002000011i3i3−i3−i3-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000
χ372222-2-2-2-222-2-22000022-2-22-2-22-22-200000022-2-222-2-222-2-20000000000000000000000000000000000000022−2−222−2−200002−22−200
χ382222-2-2-2-222-2-22000022-2-22-2-22-22-200000022-2-222-2-222-2-200000000000000000000000000000000000000−2−222−2−2220000−22−2200
χ392222-2-2-2-222-2-22000022-2-22-2-2-22-2200000022-2-2-2-222-2-2220000000000000000000000000000000000000022−2−222−2−20000−22−2200
χ402222-2-2-2-222-2-22000022-2-22-2-2-22-2200000022-2-2-2-222-2-22200000000000000000000000000000000000000−2−222−2−22200002−22−200
χ412222-2-2-2-2-2-2222000022-2-22-2-22-2-22000000-2-22222-2-2-2-2220000000000000000000000000000000000000022−2−2−2−22200002−2−2200
χ422222-2-2-2-2-2-2222000022-2-22-2-22-2-22000000-2-22222-2-2-2-22200000000000000000000000000000000000000−2−22222−2−20000−222−200
χ432222-2-2-2-2-2-2222000022-2-22-2-2-222-2000000-2-222-2-22222-2-20000000000000000000000000000000000000022−2−2−2−2220000−222−200
χ442222-2-2-2-2-2-2222000022-2-22-2-2-222-2000000-2-222-2-22222-2-200000000000000000000000000000000000000−2−22222−2−200002−2−2200
χ4522-2-2-22-2200002-22-222-22-2-2-2200000022-2-200000000000022-2-222-2-222-2-20000000000000000000000000000002-22-2002-2000000
χ4622-2-2-22-2200002-22-222-22-2-2-2200000022-2-200000000000022-2-222-2-222-2-2000000000000000000000000000000-22-2200-22000000
χ4722-2-2-22-2200002-22-222-22-2-2-22000000-2-22200000000000022-2-2-2-222-2-2220000000000000000000000000000002-22-200-22000000
χ4822-2-2-22-2200002-22-222-22-2-2-22000000-2-22200000000000022-2-2-2-222-2-222000000000000000000000000000000-22-22002-2000000
χ492-22-2-2-22200002-2-222-22-22-2-220000002-22-20000000000002-22-22-22-22-22-2000000000000000000000000002-22-200002-200000000
χ502-22-2-2-22200002-2-222-22-22-2-220000002-22-20000000000002-22-22-22-22-22-200000000000000000000000000-22-220000-2200000000
χ512-22-2-2-22200002-2-222-22-22-2-22000000-22-220000000000002-22-2-22-22-22-22000000000000000000000000002-22-20000-2200000000
χ522-22-2-2-22200002-2-222-22-22-2-22000000-22-220000000000002-22-2-22-22-22-2200000000000000000000000000-22-2200002-200000000
χ532-2-222-2-222-22-222-2-22-2-2-2-222200002-22-2-222-22-2000000002-2-222-2-222-2-2200002-2000000002-2002-22-20000000000000000000000
χ542-2-222-2-222-22-222-2-22-2-2-2-222200002-2-222-22-22-2000000002-2-22-222-2-222-20000-22000000002-200-22-220000000000000000000000
χ552-2-222-2-222-22-22-222-2-2-2-2-22220000-2200002-22-200000000-222-20000000002-20002-2002-22-2-220000002-22-2000000000000000000
χ562-2-222-2-222-22-22-222-2-2-2-2-22220000-2200002-22-200000000-222-2000000000-22000-2200-22-22-22000000-22-22000000000000000000
χ572-2-222-2-222-22-2-12-2-221111-1-1-100002-22-2-22-11-11−i3i3−i3i3−i3i3−i3i3-111-1-111-1-111-100002-200−i3i3−i3i3i3−i3-11−i3i3-11-11−i3i3i3−i3000000000000000000
χ582-2-222-2-222-22-2-12-2-221111-1-1-100002-22-2-22-11-11i3−i3i3−i3i3−i3i3−i3-111-1-111-1-111-100002-200i3−i3i3−i3−i3i3-11i3−i3-11-11i3−i3−i3i3000000000000000000
χ592-2-222-2-222-22-2-12-2-221111-1-1-100002-2-222-2-11-11−i3i3−i3i3−i3i3−i3i3-111-11-1-111-1-110000-2200−i3i3i3−i3−i3i3-11−i3i31-11-1i3−i3−i3i3000000000000000000
χ602-2-222-2-222-22-2-12-2-221111-1-1-100002-2-222-2-11-11i3−i3i3−i3i3−i3i3−i3-111-11-1-111-1-110000-2200i3−i3−i3i3i3−i3-11i3−i31-11-1−i3i3i3−i3000000000000000000
χ612-2-222-2-222-22-2-1-222-21111-1-1-10000-220000-11-11−i3i3−i3i3−i3i3−i3i31-1-11−i3i3i3−i3i3−i3−i3i302-20002-2i3−i3-11-111-1i3−i3−i3i3i3−i3-11-11000000000000000000
χ622-2-222-2-222-22-2-1-222-21111-1-1-10000-220000-11-11−i3i3−i3i3−i3i3−i3i31-1-11i3−i3−i3i3−i3i3i3−i30-22000-22i3−i31-11-11-1i3−i3i3−i3−i3i31-11-1000000000000000000
χ632-2-222-2-222-22-2-1-222-21111-1-1-10000-220000-11-11i3−i3i3−i3i3−i3i3−i31-1-11−i3i3i3−i3i3−i3−i3i30-22000-22−i3i31-11-11-1−i3i3−i3i3i3−i31-11-1000000000000000000
χ642-2-222-2-222-22-2-1-222-21111-1-1-10000-220000-11-11i3−i3i3−i3i3−i3i3−i31-1-11i3−i3−i3i3−i3i3i3−i302-20002-2−i3i3-11-111-1−i3i3i3−i3−i3i3-11-11000000000000000000
χ652-2-222-2-22-22-2222-2-22-2-2-2-22220000-222-2-22-22-22000000002-2-222-2-222-2-220000-2200000000-2200-22-220000000000000000000000
χ662-2-222-2-22-22-2222-2-22-2-2-2-22220000-22-222-2-22-22000000002-2-22-222-2-222-200002-200000000-22002-22-20000000000000000000000
χ672-2-222-2-22-22-222-222-2-2-2-2-222200002-20000-22-2200000000-222-20000000002-2000-22002-22-22-2000000-22-22000000000000000000
χ682-2-222-2-22-22-222-222-2-2-2-2-222200002-20000-22-2200000000-222-2000000000-220002-200-22-222-20000002-22-2000000000000000000
χ692-2-222-2-22-22-22-12-2-221111-1-1-10000-222-2-221-11-1−i3i3−i3i3i3−i3i3−i3-111-1-111-1-111-10000-2200i3−i3i3−i3−i3i31-1−i3i31-11-1−i3i3i3−i3000000000000000000
χ702-2-222-2-22-22-22-12-2-221111-1-1-10000-222-2-221-11-1i3−i3i3−i3−i3i3−i3i3-111-1-111-1-111-10000-2200−i3i3−i3i3i3−i31-1i3−i31-11-1i3−i3−i3i3000000000000000000
χ712-2-222-2-22-22-22-12-2-221111-1-1-10000-22-222-21-11-1−i3i3−i3i3i3−i3i3−i3-111-11-1-111-1-1100002-200i3−i3−i3i3i3−i31-1−i3i3-11-11i3−i3−i3i3000000000000000000
χ722-2-222-2-22-22-22-12-2-221111-1-1-10000-22-222-21-11-1i3−i3i3−i3−i3i3−i3i3-111-11-1-111-1-1100002-200−i3i3i3−i3−i3i31-1i3−i3-11-11−i3i3i3−i3000000000000000000
χ732-2-222-2-22-22-22-1-222-21111-1-1-100002-200001-11-1−i3i3−i3i3i3−i3i3−i31-1-11−i3i3i3−i3i3−i3−i3i30-220002-2−i3i31-11-1-11i3−i3i3−i3−i3i3-11-11000000000000000000
χ742-2-222-2-22-22-22-1-222-21111-1-1-100002-200001-11-1−i3i3−i3i3i3−i3i3−i31-1-11i3−i3−i3i3−i3i3i3−i302-2000-22−i3i3-11-11-11i3−i3−i3i3i3−i31-11-1000000000000000000
χ752-2-222-2-22-22-22-1-222-21111-1-1-100002-200001-11-1i3−i3i3−i3−i3i3−i3i31-1-11−i3i3i3−i3i3−i3−i3i302-2000-22i3−i3-11-11-11−i3i3i3−i3−i3i31-11-1000000000000000000
χ762-2-222-2-22-22-22-1-222-21111-1-1-100002-200001-11-1i3−i3i3−i3−i3i3−i3i31-1-11i3−i3−i3i3−i3i3i3−i30-220002-2i3−i31-11-1-11−i3i3−i3i3i3−i3-11-11000000000000000000
χ774444-4-4-4-444-4-4-20000-2-222-2224-44-4000000-2-222-2-222-2-22200000000000000000000000000000000000000000000000000000000
χ784444-4-4-4-444-4-4-20000-2-222-222-44-44000000-2-22222-2-222-2-200000000000000000000000000000000000000000000000000000000
χ794444-4-4-4-4-4-444-20000-2-222-2224-4-4400000022-2-2-2-22222-2-200000000000000000000000000000000000000000000000000000000
χ804444-4-4-4-4-4-444-20000-2-222-222-444-400000022-2-222-2-2-2-22200000000000000000000000000000000000000000000000000000000
χ8144-4-44-44-40000400004-4-44-44-4000000000000000000000000000000000000000000000000000000000000000022−22−22220000000000
χ8244-4-44-44-40000400004-4-44-44-40000000000000000000000000000000000000000000000000000000000000000−222222−220000000000
χ8344-4-4-44-44000044-44-44-44-4-4-440000000000000000000000-4-4440000000000000000000000000000000000000000000000000000
χ8444-4-4-44-440000-24-44-4-22-2222-2000000000000000000000022-2-2−2i3−2i32i32i32i32i3−2i3−2i300000000000000000000000000000000000000000000
χ8544-4-4-44-440000-24-44-4-22-2222-2000000000000000000000022-2-22i32i3−2i3−2i3−2i3−2i32i32i300000000000000000000000000000000000000000000
χ8644-4-4-44-440000-2-44-44-22-2222-200000044-4-4000000000000-2-222-2-222-2-22200000000000000000000000000000000000000000000
χ8744-4-4-44-440000-2-44-44-22-2222-2000000-4-444000000000000-2-22222-2-222-2-200000000000000000000000000000000000000000000
χ884-44-444-4-4000040000-444-4-44-400000000000000000000000000000000000000000000000000000000000022−22−222200000000000000
χ894-44-444-4-4000040000-444-4-44-4000000000000000000000000000000000000000000000000000000000000−222222−2200000000000000
χ904-44-4-4-4440000444-4-4-44-44-4-440000000000000000000000-44-440000000000000000000000000000000000000000000000000000
χ914-44-4-4-4440000-244-4-42-22-222-200000000000000000000002-22-2−2i32i3−2i32i32i3−2i32i3−2i300000000000000000000000000000000000000000000
χ924-44-4-4-4440000-244-4-42-22-222-200000000000000000000002-22-22i3−2i32i3−2i3−2i32i3−2i32i300000000000000000000000000000000000000000000
χ934-44-4-4-4440000-2-4-4442-22-222-20000004-44-4000000000000-22-22-22-22-22-2200000000000000000000000000000000000000000000
χ944-44-4-4-4440000-2-4-4442-22-222-2000000-44-44000000000000-22-222-22-22-22-200000000000000000000000000000000000000000000
χ954-4-44-444-44-4-4440000-4-4444-4-400000000004-4-440000000000000000000000000000000000000000000000000000000000000000
χ964-4-44-444-44-4-44-2000022-2-2-2220000000000-222-2−2i32i32i3−2i3−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000
χ974-4-44-444-44-4-44-2000022-2-2-2220000000000-222-22i3−2i3−2i32i32i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ984-4-44-444-4-444-440000-4-4444-4-40000000000-444-40000000000000000000000000000000000000000000000000000000000000000
χ994-4-44-444-4-444-4-2000022-2-2-22200000000002-2-22−2i32i32i3−2i32i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ1004-4-44-444-4-444-4-2000022-2-2-22200000000002-2-222i3−2i3−2i32i3−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000
χ10188-8-88-88-80000-40000-444-44-44000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-888-8-80000-400004-4-444-44000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).