Finite Group Databasebeta

← Group #10858333

Character table — Group #10858333

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888121212121212121224242424242424244848
order122222223444444446666666444444444412121212121212121212121212121212121212121212121244444444121212121212121212121212121212121212888888884444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ41111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-111-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ9111111111-1-1-1-11111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ10111111111-1-1-1-11111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ11111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1111-1
χ12111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-11
χ13111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-11-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111-1-11-1
χ14111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-11-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-111-11
χ15111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ16111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ172222222222222-2-2-2-2222222222220000-2-2222222222222-2-2-2-200000000-200-20000-2-20000-2-2-2-200000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-20000-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000020020000220000-2-22200000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-20000222222-2-2-2-2-2-2-2-2-2-2-2-200000000-20020000-2-20000222200000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-222000022-2-2-2-2-2-2-2-22222-2-2-2-200000000200-2000022000022-2-200000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ2222222222-122222222-1-1-1-1-1-1-12222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111112-2-22-2-2-2-2-1-11111-1-1-1-111111111000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-22222221111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2111111-1-111-1-1-1-11111000000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2221111-1-1-1-11111-1-1-1-111111111-222-2-2-22211-1-1-1-1-1-1111111-1-1-1-1000000000000000000
χ2522222222-12222-2-2-2-2-1-1-1-1-1-1-122220000-2-2-1-1-1-1-1-1-1-1-1-1-1-11111−i3−i3−i3−i3i3i3i3i3-200-2000011−i3−i3i3i31111−i3−i3i3i3−i3−i3i3i3000000000000000000
χ2622222222-12222-2-2-2-2-1-1-1-1-1-1-122220000-2-2-1-1-1-1-1-1-1-1-1-1-1-11111i3i3i3i3−i3−i3−i3−i3-200-2000011i3i3−i3−i31111i3i3−i3−i3i3i3−i3−i3000000000000000000
χ2722222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-20000-2-21111-1-1-1-111111111−i3−i3−i3−i3i3i3i3i320020000-1-1i3i3−i3−i311-1-1−i3−i3i3i3i3i3−i3−i3000000000000000000
χ2822222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-20000-2-21111-1-1-1-111111111i3i3i3i3−i3−i3−i3−i320020000-1-1−i3−i3i3i311-1-1i3i3−i3−i3−i3−i3i3i3000000000000000000
χ2922222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-22222-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1222-2-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000
χ3022222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-111111111-1-1-1-1111111112-2-2-22222-1-111111111-1-1-1-1-1-1-1-1000000000000000000
χ3122222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2222222-2-211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-22-2-22211111111-1-11111-1-1-1-1000000000000000000
χ3222222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-222-2-2-2-2-2-211111111-1-1-1-1-1-1-1-111111111-222222-2-211-1-1-1-111-1-1-1-1-1-11111000000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-2000022-1-1-1-1111111111111−i3−i3−i3−i3i3i3i3i3-2002000011−i3−i3i3i3-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-2000022-1-1-1-1111111111111i3i3i3i3−i3−i3−i3−i3-2002000011i3i3−i3−i3-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22200002211111111-1-1-1-11111−i3−i3−i3−i3i3i3i3i3200-20000-1-1i3i3−i3−i3-1-111i3i3−i3−i3−i3−i3i3i3000000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22200002211111111-1-1-1-11111i3i3i3i3−i3−i3−i3−i3200-20000-1-1−i3−i3i3i3-1-111−i3−i3i3i3i3i3−i3−i3000000000000000000
χ37222-2-22-2-22000022-2-222-2-22-2-2000022-2-20000000000000022-2-222-2-222-2-20000000000000000000000000022-2-200002-200000000
χ38222-2-22-2-22000022-2-222-2-22-2-2000022-2-20000000000000022-2-222-2-222-2-200000000000000000000000000-2-2220000-2200000000
χ39222-2-22-2-22000022-2-222-2-22-2-20000-2-2220000000000000022-2-2-2-222-2-2220000000000000000000000000022-2-20000-2200000000
χ40222-2-22-2-22000022-2-222-2-22-2-20000-2-2220000000000000022-2-2-2-222-2-22200000000000000000000000000-2-22200002-200000000
χ4122-222-2-2-2222-2-200002-222-2-2-22-22-200000022-2-222-2-222-2-2000000000000000000000000000000000000002−22−222−2−200002−22−200
χ4222-222-2-2-2222-2-200002-222-2-2-22-22-200000022-2-222-2-222-2-200000000000000000000000000000000000000−22−22−2−2220000−22−2200
χ4322-222-2-2-2222-2-200002-222-2-2-2-22-22000000-2-22222-2-2-2-222000000000000000000000000000000000000002−22−222−2−20000−22−2200
χ4422-222-2-2-2222-2-200002-222-2-2-2-22-22000000-2-22222-2-2-2-22200000000000000000000000000000000000000−22−22−2−22200002−22−200
χ4522-222-2-2-22-2-22200002-222-2-2-22-2-2200000022-2-2-2-222-2-222000000000000000000000000000000000000002−22−2−2−2220000−222−200
χ4622-222-2-2-22-2-22200002-222-2-2-22-2-2200000022-2-2-2-222-2-22200000000000000000000000000000000000000−22−2222−2−200002−2−2200
χ4722-222-2-2-22-2-22200002-222-2-2-2-222-2000000-2-222-2-22222-2-2000000000000000000000000000000000000002−22−2−2−22200002−2−2200
χ4822-222-2-2-22-2-22200002-222-2-2-2-222-2000000-2-222-2-22222-2-200000000000000000000000000000000000000−22−2222−2−20000−222−200
χ492-2-22-222-222i−2i2i−2i2-2-22-2-22-222-2000000002i−2i00002i−2i2i−2i00002-22-20000000002-20002i−2i002-22-22i−2i0000002i−2i2i−2i000000000000000000
χ502-2-22-222-222i−2i2i−2i2-2-22-2-22-222-2000000002i−2i00002i−2i2i−2i00002-22-2000000000-22000−2i2i00-22-222i−2i000000−2i2i−2i2i000000000000000000
χ512-2-22-222-222i−2i2i−2i-222-2-2-22-222-200002-22-2−2i2i00002i−2i2i−2i0000-22-222-22-22-22-200002i−2i00000000−2i2i002i−2i2i−2i0000000000000000000000
χ522-2-22-222-222i−2i2i−2i-222-2-2-22-222-20000-22-22−2i2i00002i−2i2i−2i0000-22-22-22-22-22-220000−2i2i00000000−2i2i00−2i2i−2i2i0000000000000000000000
χ532-2-22-222-22−2i2i−2i2i2-2-22-2-22-222-200000000−2i2i0000−2i2i−2i2i00002-22-20000000002-2000−2i2i002-22-2−2i2i000000−2i2i−2i2i000000000000000000
χ542-2-22-222-22−2i2i−2i2i2-2-22-2-22-222-200000000−2i2i0000−2i2i−2i2i00002-22-2000000000-220002i−2i00-22-22−2i2i0000002i−2i2i−2i000000000000000000
χ552-2-22-222-22−2i2i−2i2i-222-2-2-22-222-200002-22-22i−2i0000−2i2i−2i2i0000-22-222-22-22-22-20000−2i2i000000002i−2i00−2i2i−2i2i0000000000000000000000
χ562-2-22-222-22−2i2i−2i2i-222-2-2-22-222-20000-22-222i−2i0000−2i2i−2i2i0000-22-22-22-22-22-2200002i−2i000000002i−2i002i−2i2i−2i0000000000000000000000
χ572-2-22-222-2-12i−2i2i−2i2-2-2211-11-1-11000000002i−2i−i3i3−i3i3−ii−ii3−33−3-11-11−i3i3−i3i3i3−i3i3−i302-20002i−2i−i3i3-11-11−ii3−33−3−33−ii−ii000000000000000000
χ582-2-22-222-2-12i−2i2i−2i2-2-2211-11-1-11000000002i−2i−i3i3−i3i3−ii−ii3−33−3-11-11i3−i3i3−i3−i3i3−i3i30-22000−2i2i−i3i31-11-1−ii3−3−333−3i−ii−i000000000000000000
χ592-2-22-222-2-12i−2i2i−2i2-2-2211-11-1-11000000002i−2ii3−i3i3−i3−ii−ii−33−33-11-11−i3i3−i3i3i3−i3i3−i30-22000−2i2ii3−i31-11-1−ii−333−3−33i−ii−i000000000000000000
χ602-2-22-222-2-12i−2i2i−2i2-2-2211-11-1-11000000002i−2ii3−i3i3−i3−ii−ii−33−33-11-11i3−i3i3−i3−i3i3−i3i302-20002i−2ii3−i3-11-11−ii−33−333−3−ii−ii000000000000000000
χ612-2-22-222-2-12i−2i2i−2i-222-211-11-1-1100002-22-2−2i2i−i3i3−i3i3−ii−ii3−33−31-11-1-11-11-11-1100002i−2i00i3−i3−i3i3i3−i3i−i−33−ii−ii3−3−33000000000000000000
χ622-2-22-222-2-12i−2i2i−2i-222-211-11-1-1100002-22-2−2i2ii3−i3i3−i3−ii−ii−33−331-11-1-11-11-11-1100002i−2i00−i3i3i3−i3−i3i3i−i3−3−ii−ii−333−3000000000000000000
χ632-2-22-222-2-12i−2i2i−2i-222-211-11-1-110000-22-22−2i2i−i3i3−i3i3−ii−ii3−33−31-11-11-11-11-11-10000−2i2i00i3−i3i3−i3−i3i3i−i−33i−ii−i−333−3000000000000000000
χ642-2-22-222-2-12i−2i2i−2i-222-211-11-1-110000-22-22−2i2ii3−i3i3−i3−ii−ii−33−331-11-11-11-11-11-10000−2i2i00−i3i3−i3i3i3−i3i−i3−3i−ii−i3−3−33000000000000000000
χ652-2-22-222-2-1−2i2i−2i2i2-2-2211-11-1-1100000000−2i2i−i3i3−i3i3i−ii−i−33−33-11-11−i3i3−i3i3i3−i3i3−i302-2000−2i2i−i3i3-11-11i−i−33−333−3i−ii−i000000000000000000
χ662-2-22-222-2-1−2i2i−2i2i2-2-2211-11-1-1100000000−2i2i−i3i3−i3i3i−ii−i−33−33-11-11i3−i3i3−i3−i3i3−i3i30-220002i−2i−i3i31-11-1i−i−333−3−33−ii−ii000000000000000000
χ672-2-22-222-2-1−2i2i−2i2i2-2-2211-11-1-1100000000−2i2ii3−i3i3−i3i−ii−i3−33−3-11-11−i3i3−i3i3i3−i3i3−i30-220002i−2ii3−i31-11-1i−i3−3−333−3−ii−ii000000000000000000
χ682-2-22-222-2-1−2i2i−2i2i2-2-2211-11-1-1100000000−2i2ii3−i3i3−i3i−ii−i3−33−3-11-11i3−i3i3−i3−i3i3−i3i302-2000−2i2ii3−i3-11-11i−i3−33−3−33i−ii−i000000000000000000
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χ702-2-22-222-2-1−2i2i−2i2i-222-211-11-1-1100002-22-22i−2ii3−i3i3−i3i−ii−i3−33−31-11-1-11-11-11-110000−2i2i00−i3i3i3−i3−i3i3−ii−33i−ii−i3−3−33000000000000000000
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χ722-2-22-222-2-1−2i2i−2i2i-222-211-11-1-110000-22-222i−2ii3−i3i3−i3i−ii−i3−33−31-11-11-11-11-11-100002i−2i00−i3i3−i3i3i3−i3−ii−33−ii−ii−333−3000000000000000000
χ732-2-2-222-2220000-22-22-2-2-222-2200002-2-2200000000000000-222-22-2-222-2-220000000000000000000000000000002-22-2002-2000000
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χ914-444-4-4-44-24i−4i−4i4i00002-2-2222-200000000002i3−2i3−2i32i3−2i2i2i−2i−232323−2300000000000000000000000000000000000000000000000000000000
χ924-444-4-4-44-2−4i4i4i−4i00002-2-2222-20000000000−2i32i32i3−2i32i−2i−2i2i−232323−2300000000000000000000000000000000000000000000000000000000
χ934-444-4-4-44-2−4i4i4i−4i00002-2-2222-200000000002i3−2i3−2i32i32i−2i−2i2i23−23−232300000000000000000000000000000000000000000000000000000000
χ944-44-44-44-4400000000-44-44-44-4000000000000000000000000000000000000000000000000000000000000000022−22−22220000000000
χ954-44-44-44-4400000000-44-44-44-40000000000000000000000000000000000000000000000000000000000000000−222222−220000000000
χ964-4-4-444-44400004-44-4-4-4-444-4400000000000000000000004-4-440000000000000000000000000000000000000000000000000000
χ974-4-4-444-44-200004-44-4222-2-22-20000000000000000000000-222-2−2i32i32i3−2i32i3−2i3−2i32i300000000000000000000000000000000000000000000
χ984-4-4-444-44-200004-44-4222-2-22-20000000000000000000000-222-22i3−2i3−2i32i3−2i32i32i3−2i300000000000000000000000000000000000000000000
χ994-4-4-444-44-20000-44-44222-2-22-200004-4-44000000000000002-2-22-222-2-222-200000000000000000000000000000000000000000000
χ1004-4-4-444-44-20000-44-44222-2-22-20000-444-4000000000000002-2-222-2-222-2-2200000000000000000000000000000000000000000000
χ10188-8-8-8-888-400000000-44444-4-4000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-88-88-8-4000000004-44-44-44000000000000000000000000000000000000000000000000000000000000000000000000000000

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