Finite Group Databasebeta

← Group #10828741

Character table — Group #10828741

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size11112222222222222222444444444448888888888888888888888888888881212121216161616242424242424242424244848
order1222223444444666666622412121212121212124444444444446612121212121212121212121212121212444412121212244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ51111111111111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11-11-11111-1-1
χ61111111111111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-11-11-1-1-1-111
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
χ911111111-1-11111111111-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-11-1111-1-11-1
χ1011111111-1-11111111111-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111-11-1-1-111-11
χ1111111111-1-11111111111-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-11-11-1-111-11
χ1211111111-1-11111111111-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111-11-111-1-11-1
χ1311111111-1-11111111111-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-111-1-1-11
χ1411111111-1-11111111111-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111-1
χ1511111111-1-11111111111-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1111-1
χ1611111111-1-11111111111-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-11
χ172222222-222-2-2-22222222-2-22-2-2-2-222222-2002-2000000-2-2000000000000000000002-22-2000000000000
χ182222222-222-2-2-22222222-2-22-2-2-2-22222-2200-22000000-2-200000000000000000000-22-22000000000000
χ192222222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22-200-2200000022000000000000000000002-2-22000000000000
χ202222222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-22002-20000002200000000000000000000-222-2000000000000
χ21222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122-2-222-2-2-2-2-2-2-1-111111111111111110000-1-1-1-1000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-222-2-222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-100001111000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-11111111100001111000000000000
χ25222222-12-2-2222-1-1-1-1-1-1-1-2-2-2-1-1-1-111112222-2-2-2-222-2-211-1-1-1-11111-1-1-1-111110000-1-111000000000000
χ26222222-12-2-2222-1-1-1-1-1-1-1-2-2-2-1-1-1-1111122-2-2-2-222-2-222111111-1-1-1-11111-1-1-1-10000-1-111000000000000
χ27222222-12-2-2222-1-1-1-1-1-1-1-2-2-2-1-1-1-11111-2-22222-2-2-2-222111111-1-1-1-1-1-1-1-11111000011-1-1000000000000
χ28222222-12-2-2222-1-1-1-1-1-1-1-2-2-2-1-1-1-11111-2-2-2-2222222-2-211-1-1-1-111111111-1-1-1-1000011-1-1000000000000
χ29222222-1-222-2-2-2-1-1-1-1-1-1-1-2-221111-1-1-1-12-2002-200000011−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000-11-11000000000000
χ30222222-1-222-2-2-2-1-1-1-1-1-1-1-2-221111-1-1-1-12-2002-200000011i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000-11-11000000000000
χ31222222-1-222-2-2-2-1-1-1-1-1-1-1-2-221111-1-1-1-1-2200-2200000011−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300001-11-1000000000000
χ32222222-1-222-2-2-2-1-1-1-1-1-1-1-2-221111-1-1-1-1-2200-2200000011i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300001-11-1000000000000
χ33222222-1-2-2-2-2-2-2-1-1-1-1-1-1-122-2111111112-200-22000000-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000-111-1000000000000
χ34222222-1-2-2-2-2-2-2-1-1-1-1-1-1-122-2111111112-200-22000000-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000-111-1000000000000
χ35222222-1-2-2-2-2-2-2-1-1-1-1-1-1-122-211111111-22002-2000000-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300001-1-11000000000000
χ36222222-1-2-2-2-2-2-2-1-1-1-1-1-1-122-211111111-22002-2000000-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300001-1-11000000000000
χ372222-2-22222-2-22-2-2-2-22222-2-222-2-222-2-20000000000002-2000000000000000022-2-2000000-2020000000
χ382222-2-22222-2-22-2-2-2-22222-2-222-2-222-2-20000000000002-20000000000000000-2-22200000020-20000000
χ392222-2-222-2-2-2-22-2-2-2-2222-22222-2-2-2-222000000000000-22000000000000000022-2-200000020-20000000
χ402222-2-222-2-2-2-22-2-2-2-2222-22222-2-2-2-222000000000000-220000000000000000-2-222000000-2020000000
χ412222-2-22-22222-2-2-2-2-2222-22-2-2-22222-2-2000000000000-220000000000000000000000002-2020-2000000
χ422222-2-22-22222-2-2-2-2-2222-22-2-2-22222-2-2000000000000-22000000000000000000000000-220-202000000
χ432222-2-22-2-2-222-2-2-2-2-22222-22-2-222-2-2220000000000002-20000000000000000000000002-20-202000000
χ442222-2-22-2-2-222-2-2-2-2-22222-22-2-222-2-2220000000000002-2000000000000000000000000-22020-2000000
χ4522-2-22-22-2002-2222-2-2-22-20002-22-200000000002i−2i0000000000000000002i−2i2i−2i2i−2i2i−2i0000000000002-200
χ4622-2-22-22-2002-2222-2-2-22-20002-22-200000000002i−2i0000000000000000002i−2i2i−2i−2i2i−2i2i000000000000-2200
χ4722-2-22-22-2002-2222-2-2-22-20002-22-20000000000−2i2i000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000-2200
χ4822-2-22-22-2002-2222-2-2-22-20002-22-20000000000−2i2i000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000002-200
χ4922-2-2-222-200-222-2-222-22-20002-2-220000002i−2i0000000000000000002i−2i2i−2i00002i−2i−2i2i00000000002-20000
χ5022-2-2-222-200-222-2-222-22-20002-2-220000002i−2i0000000000000000002i−2i2i−2i0000−2i2i2i−2i0000000000-220000
χ5122-2-2-222-200-222-2-222-22-20002-2-22000000−2i2i000000000000000000−2i2i−2i2i00002i−2i−2i2i0000000000-220000
χ5222-2-2-222-200-222-2-222-22-20002-2-22000000−2i2i000000000000000000−2i2i−2i2i0000−2i2i2i−2i00000000002-20000
χ534444-4-4-2444-4-442222-2-2-24-4-4-2-222-2-222000000000000-22000000000000000000000000000000000000
χ544444-4-4-24-4-4-4-442222-2-2-2-444-2-22222-2-20000000000002-2000000000000000000000000000000000000
χ554444-4-4-2-44444-42222-2-2-2-44-422-2-2-2-2220000000000002-2000000000000000000000000000000000000
χ564444-4-4-2-4-4-444-42222-2-2-24-4422-2-222-2-2000000000000-22000000000000000000000000000000000000
χ5744-4-44-44400-44-444-4-4-44-4000-44-44000000000000000000000000000000000000000000000000000000
χ5844-4-44-4-2400-44-4-2-2222-220002-22-200000000000000000000000000000023−23−232300000000000000000000
χ5944-4-44-4-2400-44-4-2-2222-220002-22-2000000000000000000000000000000−232323−2300000000000000000000
χ6044-4-44-4-2-4004-44-2-2222-22000-22-2200000000004i−4i000000000000000000−2i2i−2i2i00000000000000000000
χ6144-4-44-4-2-4004-44-2-2222-22000-22-220000000000−4i4i0000000000000000002i−2i2i−2i00000000000000000000
χ6244-4-4-4444004-4-4-4-444-44-4000-444-4000000000000000000000000000000000000000000000000000000
χ6344-4-4-44-24004-4-422-2-22-220002-2-220000000000000000000000000023−23−2323000000000000000000000000
χ6444-4-4-44-24004-4-422-2-22-220002-2-2200000000000000000000000000−232323−23000000000000000000000000
χ6544-4-4-44-2-400-44422-2-22-22000-222-20000004i−4i000000000000000000−2i2i−2i2i000000000000000000000000
χ6644-4-4-44-2-400-44422-2-22-22000-222-2000000−4i4i0000000000000000002i−2i2i−2i000000000000000000000000
χ674-4-4400404i−4i0000000-4-4400000004i−4i00000000002-22i−2i002-22-22i−2i2i−2i0000000000000000000000000000
χ684-4-4400404i−4i0000000-4-4400000004i−4i0000000000-22−2i2i00-22-22−2i2i−2i2i0000000000000000000000000000
χ694-4-440040−4i4i0000000-4-440000000−4i4i00000000002-2−2i2i002-22-2−2i2i−2i2i0000000000000000000000000000
χ704-4-440040−4i4i0000000-4-440000000−4i4i0000000000-222i−2i00-22-222i−2i2i−2i0000000000000000000000000000
χ714-4-4400-204i−4i000−2i32i3−2i32i322-20000000−2i2i23−23000000002-22i−2i00−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ70000000000000000000000000000
χ724-4-4400-204i−4i000−2i32i3−2i32i322-20000000−2i2i23−2300000000-22−2i2i001+i3−1−i31−i3−1+i3−2ζ112ζ11−2ζ72ζ70000000000000000000000000000
χ734-4-4400-204i−4i0002i3−2i32i3−2i322-20000000−2i2i−2323000000002-22i−2i00−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ110000000000000000000000000000
χ744-4-4400-204i−4i0002i3−2i32i3−2i322-20000000−2i2i−232300000000-22−2i2i001−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ110000000000000000000000000000
χ754-4-4400-20−4i4i000−2i32i3−2i32i322-200000002i−2i−2323000000002-2−2i2i00−1−i31+i3−1+i31−i3−2ζ112ζ11−2ζ72ζ70000000000000000000000000000
χ764-4-4400-20−4i4i000−2i32i3−2i32i322-200000002i−2i−232300000000-222i−2i001+i3−1−i31−i3−1+i32ζ11−2ζ112ζ7−2ζ70000000000000000000000000000
χ774-4-4400-20−4i4i0002i3−2i32i3−2i322-200000002i−2i23−23000000002-2−2i2i00−1+i31−i3−1−i31+i3−2ζ72ζ7−2ζ112ζ110000000000000000000000000000
χ784-4-4400-20−4i4i0002i3−2i32i3−2i322-200000002i−2i23−2300000000-222i−2i001−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ110000000000000000000000000000
χ798-88-800800000000008-8-80000000000000000000000000000000000000000000000000000000000000
χ808-88-800-4000000−4i34i34i3−4i3-4440000000000000000000000000000000000000000000000000000000000000
χ818-88-800-40000004i3−4i3−4i34i3-4440000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.