Finite Group Databasebeta

← Group #10696574

Character table — Group #10696574

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888888888888888881616161616164848484848484848
order12222234466612121212444446612121212121244448888121212121212121212122424242424242424882424242422444488
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
χ511111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1111-1-1-1
χ611111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11-1-1-1111
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-1
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-111
χ92222222222222222-2-22-2-22222-2-2-2-200000000-2-2000000000000000000000002000-200
χ102222222222222222-2-22-2-22222-2-2-2-200000000-2-200000000000000000000000-2000200
χ112222222-2-2222-2-2-2-22-2-2-2222-2-222-2-222-2-200002-22222-2-2-2-20000000000000000000000
χ122222222-2-2222-2-2-2-22-2-2-2222-2-222-2-2-2-22200002-2-2-2-2-222220000000000000000000000
χ132222222-2-2222-2-2-2-2-22-22-222-2-2-2-22200000000-2200000000000000000000000002-2000
χ142222222-2-2222-2-2-2-2-22-22-222-2-2-2-22200000000-220000000000000000000000000-22000
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
χ19222222-1-2-2-1-1-111112-2-2-22-1-111-1-11122-2-20000-11-1-1-1-111113333−3−3−3−30033−3−300000000
χ20222222-1-2-2-1-1-111112-2-2-22-1-111-1-11122-2-20000-11-1-1-1-11111−3−3−3−3333300−3−33300000000
χ21222222-1-2-2-1-1-111112-2-2-22-1-111-1-111-2-2220000-111111-1-1-1-13333−3−3−3−300−3−33300000000
χ22222222-1-2-2-1-1-111112-2-2-22-1-111-1-111-2-2220000-111111-1-1-1-1−3−3−3−333330033−3−300000000
χ232222-2-222222222222-2-22-2-2-2-2-2222200000000-2-2000000000000000000000020-200000
χ242222-2-222222222222-2-22-2-2-2-2-2222200000000-2-20000000000000000000000-20200000
χ252222-2-22222222222-22-2-22-2-2-2-2-2-2-2-2000000002200000000000000002-22-22-200000000
χ262222-2-22222222222-22-2-22-2-2-2-2-2-2-2-200000000220000000000000000-22-22-2200000000
χ272222-2-22-2-2222-2-2-2-2222-2-2-2-22222-2-200000000-2200000000000000000000000000002i−2i
χ282222-2-22-2-2222-2-2-2-2222-2-2-2-22222-2-200000000-220000000000000000000000000000−2i2i
χ292222-2-22-2-2222-2-2-2-2-2-2222-2-222-2-222000022-2-22-20000000022-2-222-2-200000000000000
χ302222-2-22-2-2222-2-2-2-2-2-2222-2-222-2-2220000-2-2222-200000000-2-222-2-22200000000000000
χ312222-2-2-122-1-1-1-1-1-1-1-22-2-221111111100000000-1-133−3−333−3−333−3−3−3−3332-2-11-1100000000
χ322222-2-2-122-1-1-1-1-1-1-1-22-2-221111111100000000-1-133−3−333−3−3−3−33333−3−3-221-11-100000000
χ332222-2-2-122-1-1-1-1-1-1-1-22-2-221111111100000000-1-1−3−333−3−33333−3−3−3−333-221-11-100000000
χ342222-2-2-122-1-1-1-1-1-1-1-22-2-221111111100000000-1-1−3−333−3−333−3−33333−3−32-2-11-1100000000
χ352222-2-2-1-2-2-1-1-11111-2-222211-1-111-1-1000022-2-2-1133−3−3−3−333-1-111-1-11100−333−300000000
χ362222-2-2-1-2-2-1-1-11111-2-222211-1-111-1-1000022-2-2-11−3−33333−3−3-1-111-1-111003−3−3300000000
χ372222-2-2-1-2-2-1-1-11111-2-222211-1-111-1-10000-2-222-1133−3−3−3−33311-1-111-1-1003−3−3300000000
χ382222-2-2-1-2-2-1-1-11111-2-222211-1-111-1-10000-2-222-11−3−33333−3−311-1-111-1-100−333−300000000
χ39444444-244-2-2-2-2-2-2-2-4-44-4-4-2-2-2-222220000000022000000000000000000000000000000
χ40444444-2-4-4-2-2-22222-44-44-4-2-22222-2-2000000002-2000000000000000000000000000000
χ414444-4-4-244-2-2-2-2-2-2-24-4-44-42222-2-2-2-20000000022000000000000000000000000000000
χ424444-4-4-2-4-4-2-2-22222444-4-422-2-2-2-222000000002-2000000000000000000000000000000
χ434-44-44-44004-4-40000000004-400000000002i−2i2i−2i00000000002i−2i2i−2i2i−2i2i−2i00000000000000
χ444-44-44-44004-4-40000000004-40000000000−2i2i−2i2i0000000000−2i2i−2i2i−2i2i−2i2i00000000000000
χ454-44-44-4-200-2222323−23−2300000-2223−23000000002i−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
χ464-44-44-4-200-2222323−23−2300000-2223−2300000000−2i2i−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
χ474-44-44-4-200-222−23−23232300000-22−2323000000002i−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
χ484-44-44-4-200-222−23−23232300000-22−232300000000−2i2i−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
χ494-44-4-444004-4-4000000000-4400000000002i−2i−2i2i00000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ504-44-4-444004-4-4000000000-440000000000−2i2i2i−2i0000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ514-44-4-44-200-2222323−23−23000002-2−2323000000002i−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
χ524-44-4-44-200-2222323−23−23000002-2−232300000000−2i2i2i−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
χ534-44-4-44-200-222−23−232323000002-223−23000000002i−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
χ544-44-4-44-200-222−23−232323000002-223−2300000000−2i2i2i−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
χ554-4-440044-4-44-44-44-400000000000002-22-20000002-22-22-22-20000000000000000000000
χ564-4-440044-4-44-44-44-40000000000000-22-22000000-22-22-22-220000000000000000000000
χ574-4-44004-44-44-4-44-4400000000000002-2-220000002-22-2-22-220000000000000000000000
χ584-4-44004-44-44-4-44-440000000000000-222-2000000-22-222-22-20000000000000000000000
χ594-4-4400-24-42-22-22-2200000000023−2323−232-22-2000000−1+31−3−1−31+3−1+31−3−1−31+30000000000000000000000
χ604-4-4400-24-42-22-22-2200000000023−2323−23-22-220000001−3−1+31+3−1−31−3−1+31+3−1−30000000000000000000000
χ614-4-4400-24-42-22-22-22000000000−2323−23232-22-2000000−1−31+3−1+31−3−1−31+3−1+31−30000000000000000000000
χ624-4-4400-24-42-22-22-22000000000−2323−2323-22-220000001+3−1−31−3−1+31+3−1−31−3−1+30000000000000000000000
χ634-4-4400-2-442-222-22-200000000023−23−23232-2-22000000−1+31−3−1−31+31−3−1+31+3−1−30000000000000000000000
χ644-4-4400-2-442-222-22-200000000023−23−2323-222-20000001−3−1+31+3−1−3−1+31−3−1−31+30000000000000000000000
χ654-4-4400-2-442-222-22-2000000000−232323−232-2-22000000−1−31+3−1+31−31+3−1−31−3−1+30000000000000000000000
χ664-4-4400-2-442-222-22-2000000000−232323−23-222-20000001+3−1−31−3−1+3−1−31+3−1+31−30000000000000000000000
χ6788-8-800800-8-88000000000000000000000000000000000000000000000000000000000
χ6888-8-800-40044-443−43−434300000000000000000000000000000000000000000000000000000
χ6988-8-800-40044-4−434343−4300000000000000000000000000000000000000000000000000000

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