Finite Group Databasebeta

← Group #10692992

Character table — Group #10692992

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order1222222234444666666624444444444666612121212224466661212121212121212121212121212444444444444444444121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ7111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ8111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ9111111-1-11-1-1-1-11111111-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1i−ii−i
χ10111111-1-11-1-1-1-11111111-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1−ii−ii
χ11111111-1-11-1-1-1-11111111-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-11111iiii−i−i−i−iiiii−i−i−i−i-11-1-111−ii−ii
χ12111111-1-11-1-1-1-11111111-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-11111−i−i−i−iiiii−i−i−i−iiiii-11-1-111i−ii−i
χ13111111-1-11-1-1-1-11111111-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-11-1-111i−i−ii
χ14111111-1-11-1-1-1-11111111-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1-111−iii−i
χ15111111-1-11-1-1-1-11111111-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111111iiii−i−i−i−i−i−i−i−iiiii1-111-1-1−iii−i
χ16111111-1-11-1-1-1-11111111-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111111−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1i−i−ii
χ17222222222-2-2-2-2222222222222-2-2-2-2-2-22222-2-2-2-2000000002222-2-2-2-2-2-2000000000000000000000000000000
χ18222222222-2-2-2-222222222-2-2-2-2-2-222222222-2-2-2-200000000-2-2-2-2-2-22222000000000000000000000000000000
χ1922222222-12222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ2022222222-12222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-1-1-1-1-1-111110000000000000000-2-211110000
χ2122222222-12222-1-1-1-1-1-1-12-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-11111-1-11111-1-1-1-10000000000000000-2-211110000
χ2222222222-12222-1-1-1-1-1-1-12-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-211111111-1-111111111000000000000000022-1-1-1-10000
χ2322222222-1-2-2-2-2-1-1-1-1-1-1-122222-2-2-2-2-2-2-1-1-1-111110000−i3−i3i3i3-1-1-1-1111111−i3−i3i3i3000000000000000000−i3i3−i3i30000
χ2422222222-1-2-2-2-2-1-1-1-1-1-1-122222-2-2-2-2-2-2-1-1-1-111110000i3i3−i3−i3-1-1-1-1111111i3i3−i3−i3000000000000000000i3−i3i3−i30000
χ2522222222-1-2-2-2-2-1-1-1-1-1-1-12-2-2-2-2-2-22222-1-1-1-111110000−i3−i3i3i3111111-1-1-1-1−i3−i3i3i3000000000000000000i3−i3i3−i30000
χ2622222222-1-2-2-2-2-1-1-1-1-1-1-12-2-2-2-2-2-22222-1-1-1-111110000i3i3−i3−i3111111-1-1-1-1i3i3−i3−i3000000000000000000−i3i3−i3i30000
χ27222222-2-2222222222222-222-2-2-2-2-2-222-2-2-2-222220000000022-2-2-2-2-2-222000000000000000000000000000000
χ28222222-2-2222222222222-2-2-222-2-222-2-2-2-2-2-2222200000000-2-222-2-222-2-2000000000000000000000000000000
χ29222222-2-2-12222-1-1-1-1-1-1-1-222-2-2-2-2-2-2221111-1-1-1-10000−i3−i3i3i3-1-1111111-1-1i3i3−i3−i3000000000000000000−i3i3i3−i30000
χ30222222-2-2-12222-1-1-1-1-1-1-1-222-2-2-2-2-2-2221111-1-1-1-10000i3i3−i3−i3-1-1111111-1-1−i3−i3i3i3000000000000000000i3−i3−i3i30000
χ31222222-2-2-12222-1-1-1-1-1-1-1-2-2-222-2-222-2-21111-1-1-1-10000−i3−i3i3i311-1-111-1-111i3i3−i3−i3000000000000000000i3−i3−i3i30000
χ32222222-2-2-12222-1-1-1-1-1-1-1-2-2-222-2-222-2-21111-1-1-1-10000i3i3−i3−i311-1-111-1-111−i3−i3i3i3000000000000000000−i3i3i3−i30000
χ33222222-2-2-1-2-2-2-2-1-1-1-1-1-1-1-222-2-22222-2-21111111122-2-2-1-1-1-1-1-111-1-1-1-111111100000000000000002-2-1-1110000
χ34222222-2-2-1-2-2-2-2-1-1-1-1-1-1-1-222-2-22222-2-211111111-2-2221111-1-111-1-1-1-111-1-1-1-10000000000000000-2211-1-10000
χ35222222-2-2-1-2-2-2-2-1-1-1-1-1-1-1-2-2-22222-2-2221111111122-2-2-1-1-1-111-1-1-1-111-1-111110000000000000000-2211-1-10000
χ36222222-2-2-1-2-2-2-2-1-1-1-1-1-1-1-2-2-22222-2-22211111111-2-222111111-1-1-1-111-1-1-1-1-1-100000000000000002-2-1-1110000
χ372222-2-222222-2-22-2-2-2-222-200002-2000022-2-222-2-20000000000002-2000000000000000022-2-222-2-20000000000
χ382222-2-222222-2-22-2-2-2-222-200002-2000022-2-222-2-20000000000002-20000000000000000-2-222-2-2220000000000
χ392222-2-2222-2-2222-2-2-2-222-20000-22000022-2-2-2-222000000000000-220000000022-2-222-2-2000000000000000000
χ402222-2-2222-2-2222-2-2-2-222-20000-22000022-2-2-2-222000000000000-2200000000-2-222-2-222000000000000000000
χ412222-2-2-2-2222-2-22-2-2-2-22220000-220000-2-22222-2-2000000000000-22000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ422222-2-2-2-2222-2-22-2-2-2-22220000-220000-2-22222-2-2000000000000-2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ432222-2-2-2-22-2-2222-2-2-2-222200002-20000-2-222-2-2220000000000002-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ442222-2-2-2-22-2-2222-2-2-2-222200002-20000-2-222-2-2220000000000002-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ452-22-22-20022i−2i2i−2i-222-2-22-20002-2002i−2i0000002i−2i2i−2i00000000002-2002i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ462-22-22-20022i−2i2i−2i-222-2-22-20002-2002i−2i0000002i−2i2i−2i00000000002-2002i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ472-22-22-20022i−2i2i−2i-222-2-22-2000-2200−2i2i0000002i−2i2i−2i0000000000-2200−2i2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ482-22-22-20022i−2i2i−2i-222-2-22-2000-2200−2i2i0000002i−2i2i−2i0000000000-2200−2i2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ492-22-22-2002−2i2i−2i2i-222-2-22-20002-200−2i2i000000−2i2i−2i2i00000000002-200−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ502-22-22-2002−2i2i−2i2i-222-2-22-20002-200−2i2i000000−2i2i−2i2i00000000002-200−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ512-22-22-2002−2i2i−2i2i-222-2-22-2000-22002i−2i000000−2i2i−2i2i0000000000-22002i−2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ522-22-22-2002−2i2i−2i2i-222-2-22-2000-22002i−2i000000−2i2i−2i2i0000000000-22002i−2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ532-22-2-220022i−2i−2i2i-2-2-2222-202-20000002i−2i00002i−2i−2i2i000000002-20000002i−2i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ542-22-2-220022i−2i−2i2i-2-2-2222-202-20000002i−2i00002i−2i−2i2i000000002-20000002i−2i0000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ552-22-2-220022i−2i−2i2i-2-2-2222-20-22000000−2i2i00002i−2i−2i2i00000000-22000000−2i2i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ562-22-2-220022i−2i−2i2i-2-2-2222-20-22000000−2i2i00002i−2i−2i2i00000000-22000000−2i2i0000−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ572-22-2-22002−2i2i2i−2i-2-2-2222-202-2000000−2i2i0000−2i2i2i−2i000000002-2000000−2i2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ582-22-2-22002−2i2i2i−2i-2-2-2222-202-2000000−2i2i0000−2i2i2i−2i000000002-2000000−2i2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ592-22-2-22002−2i2i2i−2i-2-2-2222-20-220000002i−2i0000−2i2i2i−2i00000000-220000002i−2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ602-22-2-22002−2i2i2i−2i-2-2-2222-20-220000002i−2i0000−2i2i2i−2i00000000-220000002i−2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ614444-4-444-244-4-4-22222-2-2-400004-40000-2-222-2-222000000000000-220000000000000000000000000000000000
χ624444-4-444-2-4-444-22222-2-2-40000-440000-2-22222-2-20000000000002-20000000000000000000000000000000000
χ634444-4-4-4-4-244-4-4-22222-2-240000-44000022-2-2-2-2220000000000002-20000000000000000000000000000000000
χ644444-4-4-4-4-2-4-444-22222-2-2400004-4000022-2-222-2-2000000000000-220000000000000000000000000000000000
χ654-44-44-400-24i−4i4i−4i2-2-222-220004-4004i−4i000000−2i2i−2i2i0000000000-2200−2i2i00000000000000000000000000000000
χ664-44-44-400-24i−4i4i−4i2-2-222-22000-4400−4i4i000000−2i2i−2i2i00000000002-2002i−2i00000000000000000000000000000000
χ674-44-44-400-2−4i4i−4i4i2-2-222-220004-400−4i4i0000002i−2i2i−2i0000000000-22002i−2i00000000000000000000000000000000
χ684-44-44-400-2−4i4i−4i4i2-2-222-22000-44004i−4i0000002i−2i2i−2i00000000002-200−2i2i00000000000000000000000000000000
χ694-44-4-4400-24i−4i−4i4i222-2-2-2204-40000004i−4i0000−2i2i2i−2i00000000-22000000−2i2i000000000000000000000000000000
χ704-44-4-4400-24i−4i−4i4i222-2-2-220-44000000−4i4i0000−2i2i2i−2i000000002-20000002i−2i000000000000000000000000000000
χ714-44-4-4400-2−4i4i4i−4i222-2-2-2204-4000000−4i4i00002i−2i−2i2i00000000-220000002i−2i000000000000000000000000000000
χ724-44-4-4400-2−4i4i4i−4i222-2-2-220-440000004i−4i00002i−2i−2i2i000000002-2000000−2i2i000000000000000000000000000000
χ734-4-44004-440000-40000-44000000000004-40000002-22-22-22-200000000002-22-200000000000000000000000000
χ744-4-44004-440000-40000-44000000000004-4000000-22-22-22-220000000000-22-2200000000000000000000000000
χ754-4-44004-4-200002−2i32i3−2i32i32-200000000000-22−2i32i300002-22-2−1−i31+i3−1+i31−i30000000000−1−i31+i3−1+i31−i300000000000000000000000000
χ764-4-44004-4-200002−2i32i3−2i32i32-200000000000-22−2i32i30000-22-221+i3−1−i31−i3−1+i300000000001+i3−1−i31−i3−1+i300000000000000000000000000
χ774-4-44004-4-2000022i3−2i32i3−2i32-200000000000-222i3−2i300002-22-2−1+i31−i3−1−i31+i30000000000−1+i31−i3−1−i31+i300000000000000000000000000
χ784-4-44004-4-2000022i3−2i32i3−2i32-200000000000-222i3−2i30000-22-221−i3−1+i31+i3−1−i300000000001−i3−1+i31+i3−1−i300000000000000000000000000
χ794-4-4400-4440000-40000-4400000000000-440000002-2-222-22-20000000000-22-2200000000000000000000000000
χ804-4-4400-4440000-40000-4400000000000-44000000-222-2-22-2200000000002-22-200000000000000000000000000
χ814-4-4400-44-200002−2i32i3−2i32i32-2000000000002-22i3−2i300002-2-22−1−i31+i3−1+i31−i300000000001+i3−1−i31−i3−1+i300000000000000000000000000
χ824-4-4400-44-200002−2i32i3−2i32i32-2000000000002-22i3−2i30000-222-21+i3−1−i31−i3−1+i30000000000−1−i31+i3−1+i31−i300000000000000000000000000
χ834-4-4400-44-2000022i3−2i32i3−2i32-2000000000002-2−2i32i300002-2-22−1+i31−i3−1−i31+i300000000001−i3−1+i31+i3−1−i300000000000000000000000000
χ844-4-4400-44-2000022i3−2i32i3−2i32-2000000000002-2−2i32i30000-222-21−i3−1+i31+i3−1−i30000000000−1+i31−i3−1−i31+i300000000000000000000000000
χ8588-8-800008000080000-8-80000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-80000-40000-4−4i34i34i3−4i3440000000000000000000000000000000000000000000000000000000000000000000
χ8788-8-80000-40000-44i3−4i3−4i34i3440000000000000000000000000000000000000000000000000000000000000000000

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