Finite Group Databasebeta

← Group #10901327

Character table — Group #10901327

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order1222223444444666666644412121212121212124444444412121212121212121212121212121212121224661212224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-111-1-1
χ61111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-1-111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111-11-11-11-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-11-11-11-1111-1-1
χ91111111-1-111111111111-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11-111-1-111-1-1-1-1111-11-1
χ101111111-1-111111111111-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11-111-1-1-1-11111-1-1-11-11
χ111111111-1-111111111111-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-11-1-11111-1-1-1-111-11-11
χ121111111-1-111111111111-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-11-1-111-1-11111-1-11-11-1
χ131111111-1-111111111111-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-11-1-1111-1-11-111-11-1-11
χ141111111-1-111111111111-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-11-1-111-111-11-1-11-111-1
χ151111111-1-111111111111-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-1-1-111111-111-1-11-1-11-111-1-111-1
χ161111111-1-111111111111-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-1-1-111111-111-1-1-111-11-1-111-1-11
χ17222222222-2-2-2-222222222-2-22222-2-2-2-22-22-2000000000000-2-222-2-222-2-2000000000000000000
χ18222222222-2-2-2-222222222-2-22222-2-2-2-2-22-22000000000000-2-2-2-222-2-222000000000000000000
χ192222222-2-2-2-2-2-22222222-222-2-2-2-2-2-2-2-22-2-220000000000002222-2-2-2-222000000000000000000
χ202222222-2-2-2-2-2-22222222-222-2-2-2-2-2-2-2-2-222-200000000000022-2-22222-2-2000000000000000000
χ21222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-2-21111000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-11111111122-1-1-1-1000000000000
χ25222222-122-2-2-2-2-1-1-1-1-1-1-12-2-2-1-1-1-111112-22-20000−i3−i3i3i3−i3−i3i3i311-1-111-1-11100−i3i3−i3i3000000000000
χ26222222-122-2-2-2-2-1-1-1-1-1-1-12-2-2-1-1-1-111112-22-20000i3i3−i3−i3i3i3−i3−i311-1-111-1-11100i3−i3i3−i3000000000000
χ27222222-122-2-2-2-2-1-1-1-1-1-1-12-2-2-1-1-1-11111-22-220000−i3−i3i3i3−i3−i3i3i31111-1-111-1-100i3−i3i3−i3000000000000
χ28222222-122-2-2-2-2-1-1-1-1-1-1-12-2-2-1-1-1-11111-22-220000i3i3−i3−i3i3i3−i3−i31111-1-111-1-100−i3i3−i3i3000000000000
χ29222222-1-2-22222-1-1-1-1-1-1-1-2-2-21111-1-1-1-122-2-222-2-2-1-1-1-1111111-1-1-1-111112-2-1-111000000000000
χ30222222-1-2-22222-1-1-1-1-1-1-1-2-2-21111-1-1-1-122-2-2-2-2221111-1-1-1-111-1-1-1-11111-2211-1-1000000000000
χ31222222-1-2-22222-1-1-1-1-1-1-1-2-2-21111-1-1-1-1-2-22222-2-2-1-1-1-11111111111-1-1-1-1-2211-1-1000000000000
χ32222222-1-2-22222-1-1-1-1-1-1-1-2-2-21111-1-1-1-1-2-222-2-2221111-1-1-1-1111111-1-1-1-12-2-1-111000000000000
χ33222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-222111111112-2-220000−i3−i3i3i3i3i3−i3−i3-1-1-1-11111-1-100−i3i3i3−i3000000000000
χ34222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-222111111112-2-220000i3i3−i3−i3−i3−i3i3i3-1-1-1-11111-1-100i3−i3−i3i3000000000000
χ35222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-22211111111-222-20000−i3−i3i3i3i3i3−i3−i3-1-111-1-1-1-11100i3−i3−i3i3000000000000
χ36222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-22211111111-222-20000i3i3−i3−i3−i3−i3i3i3-1-111-1-1-1-11100−i3i3i3−i3000000000000
χ372222-2-22222-22-2-2-22-2-222-22-222-2-222-2-200000000000000002-20000000000000002020-20-20000
χ382222-2-22222-22-2-2-22-2-222-22-222-2-222-2-200000000000000002-2000000000000000-20-202020000
χ392222-2-2222-22-22-2-22-2-222-2-2222-2-2-2-2220000000000000000-22000000000000002020-20-200000
χ402222-2-2222-22-22-2-22-2-222-2-2222-2-2-2-2220000000000000000-2200000000000000-20-2020200000
χ412222-2-22-2-22-22-2-2-22-2-2222-22-2-22222-2-20000000000000000-2200000000000000020-2020-20000
χ422222-2-22-2-22-22-2-2-22-2-2222-22-2-22222-2-20000000000000000-22000000000000000-2020-2020000
χ432222-2-22-2-2-22-22-2-22-2-22222-2-2-222-2-22200000000000000002-20000000000000020-2020-200000
χ442222-2-22-2-2-22-22-2-22-2-22222-2-2-222-2-22200000000000000002-200000000000000-2020-20200000
χ454444-4-4-2444-44-422-222-2-2-44-4-2-222-2-2220000000000000000-2200000000000000000000000000
χ464444-4-4-244-44-4422-222-2-2-4-44-2-22222-2-200000000000000002-200000000000000000000000000
χ474444-4-4-2-4-44-44-422-222-2-24-4422-2-2-2-22200000000000000002-200000000000000000000000000
χ484444-4-4-2-4-4-44-4422-222-2-244-422-2-222-2-20000000000000000-2200000000000000000000000000
χ494-44-40044i−4i000000-4004-40004i−4i00000000002-22i−2i2-22-22i−2i2i−2i0000000000000000000000000000
χ504-44-40044i−4i000000-4004-40004i−4i0000000000-22−2i2i-22-22−2i2i−2i2i0000000000000000000000000000
χ514-44-4004−4i4i000000-4004-4000−4i4i00000000002-2−2i2i2-22-2−2i2i−2i2i0000000000000000000000000000
χ524-44-4004−4i4i000000-4004-4000−4i4i0000000000-222i−2i-22-222i−2i2i−2i0000000000000000000000000000
χ534-44-400-24i−4i0000−2i32i32−2i32i3-22000−2i2i23−23000000002-22i−2i−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ70000000000000000000000000000
χ544-44-400-24i−4i0000−2i32i32−2i32i3-22000−2i2i23−2300000000-22−2i2i1+i3−1−i31−i3−1+i3−2ζ112ζ11−2ζ72ζ70000000000000000000000000000
χ554-44-400-24i−4i00002i3−2i322i3−2i3-22000−2i2i−2323000000002-22i−2i−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ110000000000000000000000000000
χ564-44-400-24i−4i00002i3−2i322i3−2i3-22000−2i2i−232300000000-22−2i2i1−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ110000000000000000000000000000
χ574-44-400-2−4i4i0000−2i32i32−2i32i3-220002i−2i−2323000000002-2−2i2i−1−i31+i3−1+i31−i3−2ζ112ζ11−2ζ72ζ70000000000000000000000000000
χ584-44-400-2−4i4i0000−2i32i32−2i32i3-220002i−2i−232300000000-222i−2i1+i3−1−i31−i3−1+i32ζ11−2ζ112ζ7−2ζ70000000000000000000000000000
χ594-44-400-2−4i4i00002i3−2i322i3−2i3-220002i−2i23−23000000002-2−2i2i−1+i31−i3−1−i31+i3−2ζ72ζ7−2ζ112ζ110000000000000000000000000000
χ604-44-400-2−4i4i00002i3−2i322i3−2i3-220002i−2i23−2300000000-222i−2i1−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ110000000000000000000000000000
χ614-4-444-440044-4-444-4-4-4-4400000004-44-400000000000000000000000000000000000000000000
χ624-4-444-4400-4-44444-4-4-4-440000000-44-4400000000000000000000000000000000000000000000
χ634-4-444-4-20044-4-4-2-22222-20000000-22-2200000000000000000023−2323−230000000000000000000000
χ644-4-444-4-20044-4-4-2-22222-20000000-22-22000000000000000000−2323−23230000000000000000000000
χ654-4-444-4-200-4-444-2-22222-200000002-22-200000000000000000023−23−23230000000000000000000000
χ664-4-444-4-200-4-444-2-22222-200000002-22-2000000000000000000−232323−230000000000000000000000
χ674-4-44-444004-4-44-4-4-444-4400000004-4-4400000000000000000000000000000000000000000000
χ684-4-44-44400-444-4-4-4-444-440000000-444-400000000000000000000000000000000000000000000
χ694-4-44-44-2004-4-44222-2-22-20000000-222-20000000000000000000000−2i32i3−2i32i3000000000000000000
χ704-4-44-44-2004-4-44222-2-22-20000000-222-200000000000000000000002i3−2i32i3−2i3000000000000000000
χ714-4-44-44-200-444-4222-2-22-200000002-2-220000000000000000000000−2i32i32i3−2i3000000000000000000
χ724-4-44-44-200-444-4222-2-22-200000002-2-2200000000000000000000002i3−2i3−2i32i3000000000000000000
χ7388-8-800800000000800-8-80000000000000000000000000000000000000000000000000000000
χ7488-8-800-4000000−4i34i3-44i3−4i3440000000000000000000000000000000000000000000000000000000
χ7588-8-800-40000004i3−4i3-4−4i34i3440000000000000000000000000000000000000000000000000000000

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