Finite Group Databasebeta

← Group #10696085

Character table — Group #10696085

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888888888888888881616161616164848484848484848
order12222234466612121212444446612121212121244448888121212121212121212122424242424242424882424242424444488
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111
χ4111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1
χ511111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-11-111-1-1
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-11-1-111
χ922222222222222222-2-2-2-22222-2-2-2-200000000-2-2000000000000000000000000002-200
χ1022222222222222222-2-2-2-22222-2-2-2-200000000-2-200000000000000000000000000-2200
χ112222222-2-2222-2-2-2-2-22-22-222-2-2-2-222000000002-20000000000000000000000020-20000
χ122222222-2-2222-2-2-2-2-22-22-222-2-2-2-222000000002-200000000000000000000000-2020000
χ132222222-2-2222-2-2-2-2-2-22-2222-2-222-2-222-2-20000-222222-2-2-2-20000000000000000000000
χ142222222-2-2222-2-2-2-2-2-22-2222-2-222-2-2-2-2220000-22-2-2-2-222220000000000000000000000
χ15222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000
χ16222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-2111100000000
χ17222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-2111100000000
χ18222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-100000000
χ19222222-1-2-2-1-1-11111-2-22-22-1-111-1-11122-2-200001-1-1-1-1-111113333−3−3−3−30033−3−300000000
χ20222222-1-2-2-1-1-11111-2-22-22-1-111-1-11122-2-200001-1-1-1-1-11111−3−3−3−3333300−3−33300000000
χ21222222-1-2-2-1-1-11111-2-22-22-1-111-1-111-2-22200001-11111-1-1-1-13333−3−3−3−300−3−33300000000
χ22222222-1-2-2-1-1-11111-2-22-22-1-111-1-111-2-22200001-11111-1-1-1-1−3−3−3−333330033−3−300000000
χ232222-2-22222222222-22-2-22-2-2-2-2-2-2-2-2000000002200000000000000000000000000002-2
χ242222-2-22222222222-22-2-22-2-2-2-2-2-2-2-200000000220000000000000000000000000000-22
χ252222-2-22222222222-2-222-2-2-2-2-22222000022-2-2-2-20000000022-2-222-2-200000000000000
χ262222-2-22222222222-2-222-2-2-2-2-222220000-2-222-2-200000000-2-222-2-22200000000000000
χ272222-2-22-2-2222-2-2-2-2222-2-2-2-22222-2-2000000002-200000000000000002i−2i2i−2i2i−2i00000000
χ282222-2-22-2-2222-2-2-2-2222-2-2-2-22222-2-2000000002-20000000000000000−2i2i−2i2i−2i2i00000000
χ292222-2-22-2-2222-2-2-2-22-2-222-2-222-2-22200000000-22000000000000000000000020-200000
χ302222-2-22-2-2222-2-2-2-22-2-222-2-222-2-22200000000-220000000000000000000000-20200000
χ312222-2-2-122-1-1-1-1-1-1-1-2-222-21111-1-1-1-1000022-2-211−i3−i3i3i3−i3−i3i3i3-1-111-1-11100−i3i3i3−i300000000
χ322222-2-2-122-1-1-1-1-1-1-1-2-222-21111-1-1-1-1000022-2-211i3i3−i3−i3i3i3−i3−i3-1-111-1-11100i3−i3−i3i300000000
χ332222-2-2-122-1-1-1-1-1-1-1-2-222-21111-1-1-1-10000-2-22211−i3−i3i3i3−i3−i3i3i311-1-111-1-100i3−i3−i3i300000000
χ342222-2-2-122-1-1-1-1-1-1-1-2-222-21111-1-1-1-10000-2-22211i3i3−i3−i3i3i3−i3−i311-1-111-1-100−i3i3i3−i300000000
χ352222-2-2-1-2-2-1-1-11111222-2-211-1-1-1-11100000000-11−i3−i3i3i3i3i3−i3−i333−3−3−3−3332i−2i−ii−ii00000000
χ362222-2-2-1-2-2-1-1-11111222-2-211-1-1-1-11100000000-11−i3−i3i3i3i3i3−i3−i3−3−33333−3−3−2i2ii−ii−i00000000
χ372222-2-2-1-2-2-1-1-11111222-2-211-1-1-1-11100000000-11i3i3−i3−i3−i3−i3i3i333−3−3−3−333−2i2ii−ii−i00000000
χ382222-2-2-1-2-2-1-1-11111222-2-211-1-1-1-11100000000-11i3i3−i3−i3−i3−i3i3i3−3−33333−3−32i−2i−ii−ii00000000
χ39444444-244-2-2-2-2-2-2-24-4-4-4-4-2-2-2-222220000000022000000000000000000000000000000
χ40444444-2-4-4-2-2-22222-44-44-4-2-22222-2-200000000-22000000000000000000000000000000
χ414444-4-4-244-2-2-2-2-2-2-2-44-4-442222222200000000-2-2000000000000000000000000000000
χ424444-4-4-2-4-4-2-2-222224-4-44422-2-222-2-2000000002-2000000000000000000000000000000
χ434-44-40044i−4i-44-44i4i−4i−4i00000000000002-22i−2i0000002-22-22i−2i2i−2i0000000000000000000000
χ444-44-40044i−4i-44-44i4i−4i−4i0000000000000-22−2i2i000000-22-22−2i2i−2i2i0000000000000000000000
χ454-44-4004−4i4i-44-4−4i−4i4i4i00000000000002-2−2i2i0000002-22-2−2i2i−2i2i0000000000000000000000
χ464-44-4004−4i4i-44-4−4i−4i4i4i0000000000000-222i−2i000000-22-222i−2i2i−2i0000000000000000000000
χ474-44-400-24i−4i2-22−2i−2i2i2i000000000−2i32i323−232-22i−2i000000−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ484-44-400-24i−4i2-22−2i−2i2i2i000000000−2i32i323−23-22−2i2i0000001+i3−1−i31−i3−1+i3−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ494-44-400-24i−4i2-22−2i−2i2i2i0000000002i3−2i3−23232-22i−2i000000−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ504-44-400-24i−4i2-22−2i−2i2i2i0000000002i3−2i3−2323-22−2i2i0000001−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ514-44-400-2−4i4i2-222i2i−2i−2i000000000−2i32i3−23232-2−2i2i000000−1−i31+i3−1+i31−i3−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ524-44-400-2−4i4i2-222i2i−2i−2i000000000−2i32i3−2323-222i−2i0000001+i3−1−i31−i3−1+i32ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ534-44-400-2−4i4i2-222i2i−2i−2i0000000002i3−2i323−232-2−2i2i000000−1+i31−i3−1−i31+i3−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ544-44-400-2−4i4i2-222i2i−2i−2i0000000002i3−2i323−23-222i−2i0000001−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ554-4-444-4400-4-440000000004-400000000002i−2i2i−2i00000000002i−2i2i−2i2i−2i2i−2i00000000000000
χ564-4-444-4400-4-440000000004-40000000000−2i2i−2i2i0000000000−2i2i−2i2i−2i2i−2i2i00000000000000
χ574-4-444-4-20022-223−2323−2300000-2223−23000000002i−2i2i−2i0000000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000
χ584-4-444-4-20022-223−2323−2300000-2223−2300000000−2i2i−2i2i0000000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000
χ594-4-444-4-20022-2−2323−232300000-22−2323000000002i−2i2i−2i0000000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000
χ604-4-444-4-20022-2−2323−232300000-22−232300000000−2i2i−2i2i0000000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000
χ614-4-44-44400-4-44000000000-4400000000002i−2i−2i2i00000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ624-4-44-44400-4-44000000000-440000000000−2i2i2i−2i0000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ634-4-44-44-20022-223−2323−23000002-2−2323000000002i−2i−2i2i0000000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000
χ644-4-44-44-20022-223−2323−23000002-2−232300000000−2i2i2i−2i0000000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000
χ654-4-44-44-20022-2−2323−2323000002-223−23000000002i−2i−2i2i0000000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000
χ664-4-44-44-20022-2−2323−2323000002-223−2300000000−2i2i2i−2i0000000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000
χ6788-8-8008008-8-8000000000000000000000000000000000000000000000000000000000
χ6888-8-800-400-444−4i34i34i3−4i300000000000000000000000000000000000000000000000000000
χ6988-8-800-400-4444i3−4i3−4i34i300000000000000000000000000000000000000000000000000000

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