Finite Group Databasebeta

← Group #10828727

Character table — Group #10828727

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size11112222222222222222444444444448888888888888888888888888888881212121216161616242424242424242424244848
order12222222344446666666244666612121212444444444444121212121212121212121212121212121212444412121212244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ51111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11-11-11111-1-1
χ61111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-11-11-1-1-1-111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-111111-1-1
χ91111-1-111111111111111-1-1-1-1-1-1-1111111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-11-1111-1-11-1
χ101111-1-111111111111111-1-1-1-1-1-1-1111111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111-11-1-1-111-11
χ111111-1-111111111111111-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-11-11-1-111-11
χ121111-1-111111111111111-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1111-11-111-1-11-1
χ131111-1-111111111111111-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-11111-1-1-1-111-1-1-11
χ141111-1-111111111111111-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111-1
χ151111-1-111111111111111-1-1-1-1-1-1-11111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1111-1
χ161111-1-111111111111111-1-1-1-1-1-1-11111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-11
χ17222222222-2-2-2-222222222-2-22222-2-2-2-22-22-20000000000000000-2-20000000000002-22-2000000000000
χ18222222222-2-2-2-222222222-2-22222-2-2-2-2-22-220000000000000000-2-2000000000000-22-22000000000000
χ1922222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1000000000000
χ2022222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-211111111-1-1111111110000-1-1-1-1000000000000
χ2122222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-100001111000000000000
χ2222222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-11111111100001111000000000000
χ2322222222-1-2-2-2-2-1-1-1-1-1-1-12-2-2-1-1-1-111112-22-200000000−i3−i3i3i3−i3−i3i3i311−i3−i3i3i3−i3−i3i3i30000-11-11000000000000
χ2422222222-1-2-2-2-2-1-1-1-1-1-1-12-2-2-1-1-1-111112-22-200000000i3i3−i3−i3i3i3−i3−i311i3i3−i3−i3i3i3−i3−i30000-11-11000000000000
χ2522222222-1-2-2-2-2-1-1-1-1-1-1-12-2-2-1-1-1-11111-22-2200000000−i3−i3i3i3−i3−i3i3i311i3i3−i3−i3i3i3−i3−i300001-11-1000000000000
χ2622222222-1-2-2-2-2-1-1-1-1-1-1-12-2-2-1-1-1-11111-22-2200000000i3i3−i3−i3i3i3−i3−i311−i3−i3i3i3−i3−i3i3i300001-11-1000000000000
χ27222222-2-222-2-222-2-2-2-222-22-222-2-222-2-2000000000000000000002-20000000022-2-200000020-20000000
χ28222222-2-222-2-222-2-2-2-222-22-222-2-222-2-2000000000000000000002-200000000-2-222000000-2020000000
χ29222222-2-22-222-22-2-2-2-222-2-2222-2-2-2-22200000000000000000000-2200000000000000002-2020-2000000
χ30222222-2-22-222-22-2-2-2-222-2-2222-2-2-2-22200000000000000000000-220000000000000000-220-202000000
χ312222-2-2222-2-2-2-22222222-222-2-2-2-2-2-2-2-22-2-220000000000000000220000000000002-2-22000000000000
χ322222-2-2222-2-2-2-22222222-222-2-2-2-2-2-2-2-2-222-2000000000000000022000000000000-222-2000000000000
χ332222-2-222-12222-1-1-1-1-1-1-1-2-2-21111-1-1-1-122-2-222-2-222-2-2-1-1-1-1111111-1-1-1-111110000-1-111000000000000
χ342222-2-222-12222-1-1-1-1-1-1-1-2-2-21111-1-1-1-122-2-2-2-222-2-2221111-1-1-1-1111111-1-1-1-10000-1-111000000000000
χ352222-2-222-12222-1-1-1-1-1-1-1-2-2-21111-1-1-1-1-2-22222-2-2-2-2221111-1-1-1-111-1-1-1-11111000011-1-1000000000000
χ362222-2-222-12222-1-1-1-1-1-1-1-2-2-21111-1-1-1-1-2-222-2-22222-2-2-1-1-1-11111111111-1-1-1-1000011-1-1000000000000
χ372222-2-222-1-2-2-2-2-1-1-1-1-1-1-1-222111111112-2-2200000000−i3−i3i3i3i3i3−i3−i3-1-1−i3−i3i3i3i3i3−i3−i30000-111-1000000000000
χ382222-2-222-1-2-2-2-2-1-1-1-1-1-1-1-222111111112-2-2200000000i3i3−i3−i3−i3−i3i3i3-1-1i3i3−i3−i3−i3−i3i3i30000-111-1000000000000
χ392222-2-222-1-2-2-2-2-1-1-1-1-1-1-1-22211111111-222-200000000−i3−i3i3i3i3i3−i3−i3-1-1i3i3−i3−i3−i3−i3i3i300001-1-11000000000000
χ402222-2-222-1-2-2-2-2-1-1-1-1-1-1-1-22211111111-222-200000000i3i3−i3−i3−i3−i3i3i3-1-1−i3−i3i3i3i3i3−i3−i300001-1-11000000000000
χ412222-2-2-2-222-2-222-2-2-2-2222-22-2-22222-2-200000000000000000000-220000000022-2-2000000-2020000000
χ422222-2-2-2-222-2-222-2-2-2-2222-22-2-22222-2-200000000000000000000-2200000000-2-22200000020-20000000
χ432222-2-2-2-22-222-22-2-2-2-22222-2-2-222-2-222000000000000000000002-200000000000000002-20-202000000
χ442222-2-2-2-22-222-22-2-2-2-22222-2-2-222-2-222000000000000000000002-20000000000000000-22020-2000000
χ4522-2-2002-22-22-22-222-2-22-200000002-22-20000002i−2i0000000000000000002i−2i2i−2i2i−2i2i−2i0000000000002-200
χ4622-2-2002-22-22-22-222-2-22-200000002-22-20000002i−2i0000000000000000002i−2i2i−2i−2i2i−2i2i000000000000-2200
χ4722-2-2002-22-22-22-222-2-22-200000002-22-2000000−2i2i000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000-2200
χ4822-2-2002-22-22-22-222-2-22-200000002-22-2000000−2i2i000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000002-200
χ4922-2-200-222-2-222-2-2-2222-200000002-2-2200002i−2i00000000000000002i−2i2i−2i00002i−2i−2i2i00000000002-20000
χ5022-2-200-222-2-222-2-2-2222-200000002-2-2200002i−2i00000000000000002i−2i2i−2i0000−2i2i2i−2i0000000000-220000
χ5122-2-200-222-2-222-2-2-2222-200000002-2-220000−2i2i0000000000000000−2i2i−2i2i00002i−2i−2i2i0000000000-220000
χ5222-2-200-222-2-222-2-2-2222-200000002-2-220000−2i2i0000000000000000−2i2i−2i2i0000−2i2i2i−2i00000000002-20000
χ53444444-4-4-24-4-44-22222-2-2-44-4-2-222-2-22200000000000000000000-220000000000000000000000000000
χ54444444-4-4-2-444-4-22222-2-2-4-44-2-22222-2-2000000000000000000002-20000000000000000000000000000
χ554444-4-4-4-4-24-4-44-22222-2-24-4422-2-2-2-222000000000000000000002-20000000000000000000000000000
χ564444-4-4-4-4-2-444-4-22222-2-244-422-2-222-2-200000000000000000000-220000000000000000000000000000
χ5744-4-4004-444-44-4-444-4-44-40000000-44-4400000000000000000000000000000000000000000000000000
χ5844-4-4004-4-24-44-42-2-222-2200000002-22-20000000000000000000000000023−23−232300000000000000000000
χ5944-4-4004-4-24-44-42-2-222-2200000002-22-200000000000000000000000000−232323−2300000000000000000000
χ6044-4-4004-4-2-44-442-2-222-220000000-22-220000004i−4i000000000000000000−2i2i−2i2i00000000000000000000
χ6144-4-4004-4-2-44-442-2-222-220000000-22-22000000−4i4i0000000000000000002i−2i2i−2i00000000000000000000
χ6244-4-400-44444-4-4-4-4-4444-40000000-444-400000000000000000000000000000000000000000000000000
χ6344-4-400-44-244-4-4222-2-2-2200000002-2-22000000000000000000000023−23−2323000000000000000000000000
χ6444-4-400-44-244-4-4222-2-2-2200000002-2-220000000000000000000000−232323−23000000000000000000000000
χ6544-4-400-44-2-4-444222-2-2-220000000-222-200004i−4i0000000000000000−2i2i−2i2i000000000000000000000000
χ6644-4-400-44-2-4-444222-2-2-220000000-222-20000−4i4i00000000000000002i−2i2i−2i000000000000000000000000
χ674-44-44-4004000040000-4-40004-4000000000000002-22-22-22-22-22-2000000000000000000000000000000
χ684-44-44-4004000040000-4-40004-400000000000000-22-22-22-22-22-22000000000000000000000000000000
χ694-44-44-400-20000-2−2i32i3−2i32i322000-22−2i32i30000000000002-22-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3000000000000000000000000000000
χ704-44-44-400-20000-2−2i32i3−2i32i322000-22−2i32i3000000000000-22-221+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3000000000000000000000000000000
χ714-44-44-400-20000-22i3−2i32i3−2i322000-222i3−2i30000000000002-22-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3000000000000000000000000000000
χ724-44-44-400-20000-22i3−2i32i3−2i322000-222i3−2i3000000000000-22-221−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3000000000000000000000000000000
χ734-44-4-44004000040000-4-4000-44000000000000002-2-222-22-2-22-22000000000000000000000000000000
χ744-44-4-44004000040000-4-4000-4400000000000000-222-2-22-222-22-2000000000000000000000000000000
χ754-44-4-4400-20000-2−2i32i3−2i32i3220002-22i3−2i30000000000002-2-22−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i3000000000000000000000000000000
χ764-44-4-4400-20000-2−2i32i3−2i32i3220002-22i3−2i3000000000000-222-21+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i3000000000000000000000000000000
χ774-44-4-4400-20000-22i3−2i32i3−2i3220002-2−2i32i30000000000002-2-22−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i3000000000000000000000000000000
χ784-44-4-4400-20000-22i3−2i32i3−2i3220002-2−2i32i3000000000000-222-21−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i3000000000000000000000000000000
χ798-8-88000080000-80000-880000000000000000000000000000000000000000000000000000000000000
χ808-8-880000-400004−4i34i34i3−4i34-40000000000000000000000000000000000000000000000000000000000000
χ818-8-880000-4000044i3−4i3−4i34i34-40000000000000000000000000000000000000000000000000000000000000

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