Finite Group Databasebeta

← Group #72254886

Character table — Group #72254886

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222444444444488888888888888816161616161616161616161616161616161616161624242424242432323232323232324848484848484848489696
order12222236662244446666222222666661212121244444446666121212121212121212122222444412121212121244444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-111111111111-1-1-1111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-11-11-11111-1-1
χ61111111111111111111111-1-111111111111-1-1-1111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-111
χ71111111111111111111111-1-111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-11-11-1-1-1-1-111
χ81111111111111111111111-1-111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111-11-111111-1-1
χ91111111111-1-111-1-111-1-11111-1-111-1-1-111-1-1-1-11ii−i−i1-111-1-1iiii−i−i−i−i111111i−i1-1ii−i−i-1-1-1-11ii−i−ii−i
χ101111111111-1-111-1-111-1-11111-1-111-1-1-111-1-1-1-11ii−i−i1-111-1-1iiii−i−i−i−i-1-1-1-1-1-1i−i1-1ii−i−i1111-1−i−iii−ii
χ111111111111-1-111-1-111-1-11111-1-111-1-1-111-1-1-1-11−i−iii1-111-1-1−i−i−i−iiiii111111−ii1-1−i−iii-1-1-1-11−i−iii−ii
χ121111111111-1-111-1-111-1-11111-1-111-1-1-111-1-1-1-11−i−iii1-111-1-1−i−i−i−iiiii-1-1-1-1-1-1−ii1-1−i−iii1111-1ii−i−ii−i
χ131111111111-1-111-1-111-1-111-1-1-1-111-1-1-111-1-111-1ii−i−i1-1-1-111iiii−i−i−i−i11-1-111−ii-11−i−iii1-11-1-1ii−i−i−ii
χ141111111111-1-111-1-111-1-111-1-1-1-111-1-1-111-1-111-1ii−i−i1-1-1-111iiii−i−i−i−i-1-111-1-1−ii-11−i−iii-11-111−i−iiii−i
χ151111111111-1-111-1-111-1-111-1-1-1-111-1-1-111-1-111-1−i−iii1-1-1-111−i−i−i−iiiii11-1-111i−i-11ii−i−i1-11-1-1−i−iiii−i
χ161111111111-1-111-1-111-1-111-1-1-1-111-1-1-111-1-111-1−i−iii1-1-1-111−i−i−i−iiiii-1-111-1-1i−i-11ii−i−i-11-111ii−i−i−ii
χ1722222222222222222222-2-200-2-2-2-22-2-222220000000-2-20000000000002200-2-200000000020-20000000
χ1822222222222222222222-2-200-2-2-2-22-2-222220000000-2-2000000000000-2-20022000000000-2020000000
χ19222222222222-2-2-2-222222-200-22-2-22-2-2-2-2-2-20000000220000000000000022000000000020-20-2000000
χ20222222222222-2-2-2-222222-200-22-2-22-2-2-2-2-2-200000002200000000000000-2-20000000000-20202000000
χ21222222222222-2-2-2-22222-22222-222222-2-2-2-22-2-20000-2-222220000000000000000-2-2000000000000000
χ22222222222222-2-2-2-22222-22-2-22-222222-2-2-2-2-2220000-2-2-2-2-2-2000000000000000022000000000000000
χ232222222222-2-222-2-222-2-2-2-20022-2-2-22222-2-20000000-220000000000002200-2-2000000000-2020000000
χ242222222222-2-222-2-222-2-2-2-20022-2-2-22222-2-20000000-22000000000000-2-2002200000000020-20000000
χ252222222222-2-2-2-22222-2-22-2002-2-2-2-222-2-22200000002-200000000000000220000000000-2020-2000000
χ262222222222-2-2-2-22222-2-22-2002-2-2-2-222-2-22200000002-200000000000000-2-2000000000020-202000000
χ272222222222-2-2-2-22222-2-2-2222-2222-2-2-2-2-222-22-20000-2222-2-20000000000000000-22000000000000000
χ282222222222-2-2-2-22222-2-2-22-2-2-2222-2-2-2-2-2222-220000-22-2-22200000000000000002-2000000000000000
χ29222222-1-1-1-1222222-1-1-1-1222222-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-100000000000
χ30222222-1-1-1-1222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-111111111000000-2-2-1-1111100000000000
χ31222222-1-1-1-1222222-1-1-1-122-2-222-1-1-1-1-1-1-1-1-1-2-2-22222-1-11111-1-1-1-1-1-1-1-1000000-2-211111100000000000
χ32222222-1-1-1-1222222-1-1-1-122-2-222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-1-11111111111110000002211-1-1-1-100000000000
χ33222222-1-1-1-122-2-2-2-2-1-1-1-1-22222-2-1-1-1-1-111112-2-2000011-1-1-1-1−i3−i3i3i3−i3−i3i3i30000000011−i3i3−i3i300000000000
χ34222222-1-1-1-122-2-2-2-2-1-1-1-1-22222-2-1-1-1-1-111112-2-2000011-1-1-1-1i3i3−i3−i3i3i3−i3−i30000000011i3−i3i3−i300000000000
χ35222222-1-1-1-122-2-2-2-2-1-1-1-1-22-2-22-2-1-1-1-1-11111-2220000111111−i3−i3i3i3−i3−i3i3i300000000-1-1i3−i3i3−i300000000000
χ36222222-1-1-1-122-2-2-2-2-1-1-1-1-22-2-22-2-1-1-1-1-11111-2220000111111i3i3−i3−i3i3i3−i3−i300000000-1-1−i3i3−i3i300000000000
χ37222222-1-1-1-1-2-222-2-2-1-1112222-2-2-1-1111-1-111-2-222i2i−2i−2i-11-1-111−i−i−i−iiiii0000002i−2i-11−i−iii00000000000
χ38222222-1-1-1-1-2-222-2-2-1-1112222-2-2-1-1111-1-111-2-22−2i−2i2i2i-11-1-111iiii−i−i−i−i000000−2i2i-11ii−i−i00000000000
χ39222222-1-1-1-1-2-222-2-2-1-11122-2-2-2-2-1-1111-1-11122-22i2i−2i−2i-1111-1-1−i−i−i−iiiii000000−2i2i1-1ii−i−i00000000000
χ40222222-1-1-1-1-2-222-2-2-1-11122-2-2-2-2-1-1111-1-11122-2−2i−2i2i2i-1111-1-1iiii−i−i−i−i0000002i−2i1-1−i−iii00000000000
χ41222222-1-1-1-1-2-2-2-222-1-111-2222-22-1-111111-1-1-22-200001-1-1-11133−3−3−3−333000000001-13−3−3300000000000
χ42222222-1-1-1-1-2-2-2-222-1-111-2222-22-1-111111-1-1-22-200001-1-1-111−3−33333−3−3000000001-1−333−300000000000
χ43222222-1-1-1-1-2-2-2-222-1-111-22-2-2-22-1-111111-1-12-2200001-111-1-133−3−3−3−33300000000-11−333−300000000000
χ44222222-1-1-1-1-2-2-2-222-1-111-22-2-2-22-1-111111-1-12-2200001-111-1-1−3−33333−3−300000000-113−3−3300000000000
χ45444444-2-2-2-2444444-2-2-2-2-4-400-4-422-222-2-2-2-20000000220000000000000000000000000000000000000
χ46444444-2-2-2-244-4-4-4-4-2-2-2-24-400-4422-22222220000000-2-20000000000000000000000000000000000000
χ47444444-2-2-2-2-4-444-4-4-2-222-4-40044222-2-2-2-22200000002-20000000000000000000000000000000000000
χ48444444-2-2-2-2-4-4-4-444-2-2224-4004-4222-2-222-2-20000000-220000000000000000000000000000000000000
χ494444-4-444444-40000-4-4-4-40000000040000000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000
χ504444-4-444444-40000-4-4-4-4000000004000000000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000
χ514444-4-44444-440000-4-44400000000-40000000002-2-220000002-22-2-22-220000000000000000000000000
χ524444-4-44444-440000-4-44400000000-4000000000-222-2000000-22-222-22-20000000000000000000000000
χ534444-4-4-2-2-2-24-400002222000000−2i32i3-2−2i32i300000002i−2i2i−2i0000002ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ110000000000000000000000000
χ544444-4-4-2-2-2-24-400002222000000−2i32i3-2−2i32i30000000−2i2i−2i2i000000−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ110000000000000000000000000
χ554444-4-4-2-2-2-24-4000022220000002i3−2i3-22i3−2i300000002i−2i2i−2i0000002ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ70000000000000000000000000
χ564444-4-4-2-2-2-24-4000022220000002i3−2i3-22i3−2i30000000−2i2i−2i2i000000−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ70000000000000000000000000
χ574444-4-4-2-2-2-2-44000022-2-2000000−2i32i322i3−2i300000002-2-22000000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i30000000000000000000000000
χ584444-4-4-2-2-2-2-44000022-2-2000000−2i32i322i3−2i30000000-222-20000001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i30000000000000000000000000
χ594444-4-4-2-2-2-2-44000022-2-20000002i3−2i32−2i32i300000002-2-22000000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i30000000000000000000000000
χ604444-4-4-2-2-2-2-44000022-2-20000002i3−2i32−2i32i30000000-222-20000001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i30000000000000000000000000
χ614-4-444-44-44-400004-44-40000000000000004-400000000000000000000000000000000000000002i−2i2i−2i00
χ624-4-444-44-44-400004-44-40000000000000004-40000000000000000000000000000000000000000−2i2i−2i2i00
χ634-4-444-44-44-40000-444-4000000000000000-4400000000000000000000000000000000000000002-2-2200
χ644-4-444-44-44-40000-444-4000000000000000-440000000000000000000000000000000000000000-222-200
χ654-4-44-444-44-4004-400-4400000000000004-40000000000000000000000000004-40000000000000000000
χ664-4-44-444-44-4004-400-4400000000000004-4000000000000000000000000000-440000000000000000000
χ674-4-44-444-44-400-4400-440000000000000-44000000000000000000000004-400000000000000000000000
χ684-4-44-444-44-400-4400-440000000000000-4400000000000000000000000-4400000000000000000000000
χ6988-8-8008-8-880000000000004-4000000000000000000004-400000000000000000000000000000000000
χ7088-8-8008-8-88000000000000-4400000000000000000000-4400000000000000000000000000000000000
χ7188-8-800-444-400000000−4i34i3004-400000000000000000000-22−2i32i3000000000000000000000000000000000
χ7288-8-800-444-400000000−4i34i300-44000000000000000000002-22i3−2i3000000000000000000000000000000000
χ7388-8-800-444-4000000004i3−4i3004-400000000000000000000-222i3−2i3000000000000000000000000000000000
χ7488-8-800-444-4000000004i3−4i300-44000000000000000000002-2−2i32i3000000000000000000000000000000000
χ758-88-80088-8-80000000000000000000000000000000000000000000000004-4000000000000000000000
χ768-88-80088-8-8000000000000000000000000000000000000000000000000-44000000000000000000000
χ778-8-888-8-44-4400008-8-44000000000000000-440000000000000000000000000000000000000000000000
χ788-8-888-8-44-440000-88-440000000000000004-40000000000000000000000000000000000000000000000
χ798-8-88-88-44-44008-8004-40000000000000-44000000000000000000000000000000000000000000000000
χ808-8-88-88-44-4400-88004-400000000000004-4000000000000000000000000000000000000000000000000
χ8116-1616-1600-8-88800000000000000000000000000000000000000000000000000000000000000000000000

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