Finite Group Databasebeta

← Group #10740360

Character table — Group #10740360

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111111111111122222222222222224444444488888888888888888888888888888888888888121212121212121212121212121212122424242424242424
order12222222222222223666666666666666444444442222444444666666661212121212121212121212121212121212121212444444444444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1
χ911111111111111111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1
χ1011111111111111111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ1111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111
χ1211111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ172222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ182222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-2-2-2-2-2-2-2-2-1-1-1-11111-1-1-1-111111111-1-1-1-11111000000000000000000000000
χ192222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-22222-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000
χ202222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-2-2222211111111-1-1-1-11111-1-1-1-11111-1-1-1-1000000000000000000000000
χ212222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-222-2-222-2-21111-1-1-1-111111111-1-1-1-1-1-1-1-11111000000000000000000000000
χ222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-222-2-222111111111111-1-1-1-11111-1-1-1-1-1-1-1-1000000000000000000000000
χ232222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-222-1-1-1-1-1-1-1-11111111111111111-1-1-1-1000000000000000000000000
χ242222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-22222-2-2-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000000000000000
χ2522222-22-22-2-2-2-2-2-22222222-2-2-2-2-2-22-2-2200000000000000002-200000000000000000000000022-2-200002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222-22-22-2-2-2-2-2-22222222-2-2-2-2-2-22-2-2200000000000000002-200000000000000000000000022-2-20000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222-22-22-2-2-2-2-2-22222222-2-2-2-2-2-22-2-220000000000000000-22000000000000000000000000-2-22200002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222-22-22-2-2-2-2-2-22222222-2-2-2-2-2-22-2-220000000000000000-22000000000000000000000000-2-2220000−2i−2i2i2i2i2i−2i−2i000000000000
χ292222-2-2-2-2-2222-2-22-22222-2-2222-2-2-2-22-2-22i2i−2i−2i00000000000000000000002i2i−2i−2i00000000000000002i2i−2i−2i0000000000002-2000000
χ302222-2-2-2-2-2222-2-22-22222-2-2222-2-2-2-22-2-22i2i−2i−2i00000000000000000000002i2i−2i−2i0000000000000000−2i−2i2i2i000000000000-22000000
χ312222-2-2-2-2-2222-2-22-22222-2-2222-2-2-2-22-2-2−2i−2i2i2i0000000000000000000000−2i−2i2i2i00000000000000002i2i−2i−2i000000000000-22000000
χ322222-2-2-2-2-2222-2-22-22222-2-2222-2-2-2-22-2-2−2i−2i2i2i0000000000000000000000−2i−2i2i2i0000000000000000−2i−2i2i2i0000000000002-2000000
χ3322-2-22222-22-2-2-2-22-222-2-22-22-2-22-2-2222-20000000000002-2000000000000000022-2-20000000000002i−2i2i−2i00002i−2i2i−2i000000000000
χ3422-2-22222-22-2-2-2-22-222-2-22-22-2-22-2-2222-20000000000002-2000000000000000022-2-2000000000000−2i2i−2i2i0000−2i2i−2i2i000000000000
χ3522-2-22222-22-2-2-2-22-222-2-22-22-2-22-2-2222-2000000000000-220000000000000000-2-2220000000000002i−2i2i−2i0000−2i2i−2i2i000000000000
χ3622-2-22222-22-2-2-2-22-222-2-22-22-2-22-2-2222-2000000000000-220000000000000000-2-222000000000000−2i2i−2i2i00002i−2i2i−2i000000000000
χ3722-2-22-22-2-2-22222-2-222-2-22-2-222-2222-2-2-200002i2i−2i−2i0000000000000000000000000000002i2i−2i−2i0000000000002-2-2200000000002i−2i
χ3822-2-22-22-2-2-22222-2-222-2-22-2-222-2222-2-2-200002i2i−2i−2i0000000000000000000000000000002i2i−2i−2i000000000000-222-20000000000−2i2i
χ3922-2-22-22-2-2-22222-2-222-2-22-2-222-2222-2-2-20000−2i−2i2i2i000000000000000000000000000000−2i−2i2i2i0000000000002-2-220000000000−2i2i
χ4022-2-22-22-2-2-22222-2-222-2-22-2-222-2222-2-2-20000−2i−2i2i2i000000000000000000000000000000−2i−2i2i2i000000000000-222-200000000002i−2i
χ4122-2-2-2-2-2-222-2-2222222-2-2-222-2-2-222-22-2200000000002-2000000000022-2-2000000000000000000002-2-220000000022-2-200000000
χ4222-2-2-2-2-2-222-2-2222222-2-2-222-2-2-222-22-2200000000002-2000000000022-2-200000000000000000000-222-200000000-2-22200000000
χ4322-2-2-2-2-2-222-2-2222222-2-2-222-2-2-222-22-220000000000-220000000000-2-222000000000000000000002-2-2200000000-2-22200000000
χ4422-2-2-2-2-2-222-2-2222222-2-2-222-2-2-222-22-220000000000-220000000000-2-22200000000000000000000-222-20000000022-2-200000000
χ452-22-222-2-22-22-22-22-22-22-222-22-222-2-22-2-22i−2i2i−2i00000000000000000000002i−2i2i−2i000000000000000000002i−2i2i−2i00000000002-20000
χ462-22-222-2-22-22-22-22-22-22-222-22-222-2-22-2-22i−2i2i−2i00000000000000000000002i−2i2i−2i00000000000000000000−2i2i−2i2i0000000000-220000
χ472-22-222-2-22-22-22-22-22-22-222-22-222-2-22-2-2−2i2i−2i2i0000000000000000000000−2i2i−2i2i000000000000000000002i−2i2i−2i0000000000-220000
χ482-22-222-2-22-22-22-22-22-22-222-22-222-2-22-2-2−2i2i−2i2i0000000000000000000000−2i2i−2i2i00000000000000000000−2i2i−2i2i00000000002-20000
χ492-22-22-2-2222-22-22-2-22-22-2222-22-2-22-2-22-2000000000000002i−2i0000000000000000002i2i−2i−2i0000000000002-2-2200002i−2i2i−2i00000000
χ502-22-22-2-2222-22-22-2-22-22-2222-22-2-22-2-22-2000000000000002i−2i0000000000000000002i2i−2i−2i000000000000-222-20000−2i2i−2i2i00000000
χ512-22-22-2-2222-22-22-2-22-22-2222-22-2-22-2-22-200000000000000−2i2i000000000000000000−2i−2i2i2i0000000000002-2-220000−2i2i−2i2i00000000
χ522-22-22-2-2222-22-22-2-22-22-2222-22-2-22-2-22-200000000000000−2i2i000000000000000000−2i−2i2i2i000000000000-222-200002i−2i2i−2i00000000
χ532-22-2-2-222-2-22-2-22222-22-2-2-2-22-2-2-2222222-2-222-22-22-20000000022-2-200002-2-22000000002-22-20000000000000000000000000000
χ542-22-2-2-222-2-22-2-22222-22-2-2-2-22-2-2-2222222-2-22-22-22-2200000000-2-22200002-2-2200000000-22-220000000000000000000000000000
χ552-22-2-2-222-2-22-2-22222-22-2-2-2-22-2-2-222222-222-22-22-2-2200000000-2-2220000-222-2000000002-22-20000000000000000000000000000
χ562-22-2-2-222-2-22-2-22222-22-2-2-2-22-2-2-222222-222-2-22-222-20000000022-2-20000-222-200000000-22-220000000000000000000000000000
χ572-22-2-2-222-2-22-2-2222-11-11111-1111-1-1-1-1-12-2-222-22-22-200000000-1-111−i3i3−i3i3-111-1−i3i3−i3i3−i3i3−i3i3-11-11−i3i3−i3i3000000000000000000000000
χ582-22-2-2-222-2-22-2-2222-11-11111-1111-1-1-1-1-12-2-222-22-22-200000000-1-111i3−i3i3−i3-111-1i3−i3i3−i3i3−i3i3−i3-11-11i3−i3i3−i3000000000000000000000000
χ592-22-2-2-222-2-22-2-2222-11-11111-1111-1-1-1-1-12-2-22-22-22-220000000011-1-1−i3i3−i3i3-111-1−i3i3−i3i3i3−i3i3−i31-11-1i3−i3i3−i3000000000000000000000000
χ602-22-2-2-222-2-22-2-2222-11-11111-1111-1-1-1-1-12-2-22-22-22-220000000011-1-1i3−i3i3−i3-111-1i3−i3i3−i3−i3i3−i3i31-11-1−i3i3−i3i3000000000000000000000000
χ612-22-2-2-222-2-22-2-2222-11-11111-1111-1-1-1-1-1-222-22-22-2-220000000011-1-1−i3i3−i3i31-1-11i3−i3i3−i3−i3i3−i3i3-11-11i3−i3i3−i3000000000000000000000000
χ622-22-2-2-222-2-22-2-2222-11-11111-1111-1-1-1-1-1-222-22-22-2-220000000011-1-1i3−i3i3−i31-1-11−i3i3−i3i3i3−i3i3−i3-11-11−i3i3−i3i3000000000000000000000000
χ632-22-2-2-222-2-22-2-2222-11-11111-1111-1-1-1-1-1-222-2-22-222-200000000-1-111−i3i3−i3i31-1-11i3−i3i3−i3i3−i3i3−i31-11-1−i3i3−i3i3000000000000000000000000
χ642-22-2-2-222-2-22-2-2222-11-11111-1111-1-1-1-1-1-222-2-22-222-200000000-1-111i3−i3i3−i31-1-11−i3i3−i3i3−i3i3−i3i31-11-1i3−i3i3−i3000000000000000000000000
χ652-2-22-222-2222-2-22-2-22-2-22-2222-22-222-2-2-200002i−2i−2i2i0000000000000000000000000000002i−2i−2i2i00000000000000002i−2i−2i2i00002-200
χ662-2-22-222-2222-2-22-2-22-2-22-2222-22-222-2-2-200002i−2i−2i2i0000000000000000000000000000002i−2i−2i2i0000000000000000−2i2i2i−2i0000-2200
χ672-2-22-222-2222-2-22-2-22-2-22-2222-22-222-2-2-20000−2i2i2i−2i000000000000000000000000000000−2i2i2i−2i00000000000000002i−2i−2i2i0000-2200
χ682-2-22-222-2222-2-22-2-22-2-22-2222-22-222-2-2-20000−2i2i2i−2i000000000000000000000000000000−2i2i2i−2i0000000000000000−2i2i2i−2i00002-200
χ6944444-44-44-4-4-4-4-4-44-2-2-2-2-2-2222222-222-200000000000000004-4000000000000000000000000-2-222000000000000000000000000
χ7044444-44-44-4-4-4-4-4-44-2-2-2-2-2-2222222-222-20000000000000000-4400000000000000000000000022-2-2000000000000000000000000
χ714444-44-44-4-4-4-444-4-44444-4-4-4-4-4444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ724444-44-44-4-4-4-444-4-4-2-2-2-222222-2-2-222-22000000000000000000000000000000000023−23−232300000000000000000000000000000000
χ734444-44-44-4-4-4-444-4-4-2-2-2-222222-2-2-222-220000000000000000000000000000000000−232323−2300000000000000000000000000000000
χ744444-4-4-4-4-4444-4-44-4-2-2-2-222-2-2-22222-2224i4i−4i−4i0000000000000000000000−2i−2i2i2i0000000000000000000000000000000000000000
χ754444-4-4-4-4-4444-4-44-4-2-2-2-222-2-2-22222-222−4i−4i4i4i00000000000000000000002i2i−2i−2i0000000000000000000000000000000000000000
χ7644-4-44444-44-4-4-4-44-4-2-222-22-222-222-2-2-220000000000004-40000000000000000-2-222000000000000000000000000000000000000
χ7744-4-44444-44-4-4-4-44-4-2-222-22-222-222-2-2-22000000000000-44000000000000000022-2-2000000000000000000000000000000000000
χ7844-4-44-44-4-4-44444-4-4-2-222-222-2-22-2-2-222200004i4i−4i−4i000000000000000000000000000000−2i−2i2i2i0000000000000000000000000000
χ7944-4-44-44-4-4-44444-4-4-2-222-222-2-22-2-2-22220000−4i−4i4i4i0000000000000000000000000000002i2i−2i−2i0000000000000000000000000000
χ8044-4-4-44-444-444-4-4-4444-4-4-44-4444-4-4-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ8144-4-4-44-444-444-4-4-44-2-2222-22-2-2-22222-2-2000000000000000000−2i32i3−2i32i3000000000000000000000000000000000000000000000000
χ8244-4-4-44-444-444-4-4-44-2-2222-22-2-2-22222-2-20000000000000000002i3−2i32i3−2i3000000000000000000000000000000000000000000000000
χ8344-4-4-4-4-4-444-4-44444-2-2222-2-2222-2-22-22-200000000004-40000000000-2-22200000000000000000000000000000000000000000000
χ8444-4-4-4-4-4-444-4-44444-2-2222-2-2222-2-22-22-20000000000-44000000000022-2-200000000000000000000000000000000000000000000
χ854-44-444-4-44-44-44-44-4-22-22-2-22-22-2-222-2224i−4i4i−4i0000000000000000000000−2i2i−2i2i0000000000000000000000000000000000000000
χ864-44-444-4-44-44-44-44-4-22-22-2-22-22-2-222-222−4i4i−4i4i00000000000000000000002i−2i2i−2i0000000000000000000000000000000000000000
χ874-44-44-4-4444-44-44-4-4-22-22-2-2-22-222-222-22000000000000004i−4i000000000000000000−2i−2i2i2i00000000000000000000000000000000
χ884-44-44-4-4444-44-44-4-4-22-22-2-2-22-222-222-2200000000000000−4i4i0000000000000000002i2i−2i−2i00000000000000000000000000000000
χ894-44-4-444-4-44-444-4-444-44-4-4-44-4444-44-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ904-44-4-444-4-44-444-4-44-22-2222-22-2-2-22-222-2000000000000000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ914-44-4-444-4-44-444-4-44-22-2222-22-2-2-22-222-20000000000000000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000
χ924-4-4444-4-4-4-4-44-44444-4-444-4-4-444-44-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ934-4-4444-4-4-4-4-44-4444-222-2-2222-2-22-22-22-20000000000000000000000−2i32i32i3−2i300000000000000000000000000000000000000000000
χ944-4-4444-4-4-4-4-44-4444-222-2-2222-2-22-22-22-200000000000000000000002i3−2i3−2i32i300000000000000000000000000000000000000000000
χ954-4-444-4-44-444-44-4-444-4-444-444-4-44-4-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ964-4-444-4-44-444-44-4-44-222-2-22-2-222-2222-2-2000000000000000000−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ974-4-444-4-44-444-44-4-44-222-2-22-2-222-2222-2-20000000000000000002i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ984-4-44-444-4444-4-44-4-4-222-22-2-2-22-22-2-222200004i−4i−4i4i000000000000000000000000000000−2i2i2i−2i0000000000000000000000000000
χ994-4-44-444-4444-4-44-4-4-222-22-2-2-22-22-2-22220000−4i4i4i−4i0000000000000000000000000000002i−2i−2i2i0000000000000000000000000000
χ1004-4-44-4-4444-4-444-44-44-4-44-44-4-44-44-4444-40000000000000000000000000000000000000000000000000000000000000000000000
χ1014-4-44-4-4444-4-444-44-4-222-22-222-22-22-2-2-22000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ1024-4-44-4-4444-4-444-44-4-222-22-222-22-22-2-2-220000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000000000000000

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