Finite Group Databasebeta

← Group #10696071

Character table — Group #10696071

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888888888888888881616161616164848484848484848
order1222223446661212121244444661212121212122244666688881212121212122424242424242424882424242424444488
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ41111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ511111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1
χ811111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111
χ92222222222222222-2-22-2-222-2-222-2-2000000000000-2-200000000000000000000002-200
χ102222222222222222-2-22-2-222-2-222-2-2000000000000-2-20000000000000000000000-2200
χ112222222-2-2222-2-2-2-22-2-22-222-2-2-2-2220000000000002-2000000000000000000002-20000
χ122222222-2-2222-2-2-2-22-2-22-222-2-2-2-2220000000000002-200000000000000000000-220000
χ132222222-2-2222-2-2-2-2-22-2-222222-2-2-2-222-2-222220000-22-2-2-2-20000000000000000000000
χ142222222-2-2222-2-2-2-2-22-2-222222-2-2-2-2-2-222-2-2-2-20000-2222220000000000000000000000
χ15222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000
χ16222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111-2-2111100000000
χ17222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-1-2-2111100000000
χ18222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-111111111111122-1-1-1-100000000
χ19222222-1-2-2-1-1-11111-22-2-22-1-1-1-1111122-2-2-1-1-1-100001-111113333−3−3−3−30033−3−300000000
χ20222222-1-2-2-1-1-11111-22-2-22-1-1-1-1111122-2-2-1-1-1-100001-11111−3−3−3−3333300−3−33300000000
χ21222222-1-2-2-1-1-11111-22-2-22-1-1-1-11111-2-222111100001-1-1-1-1-13333−3−3−3−300−3−33300000000
χ22222222-1-2-2-1-1-11111-22-2-22-1-1-1-11111-2-222111100001-1-1-1-1-1−3−3−3−333330033−3−300000000
χ232222-2-222222222222-2-2-22-2-2-2-2-2-2-2-2000000000000220000000000000000000000002-2
χ242222-2-222222222222-2-2-22-2-2-2-2-2-2-2-200000000000022000000000000000000000000-22
χ252222-2-22222222222-22-22-2-2-222-2-2220000000022-2-2-2-2000022-2-222-2-200000000000000
χ262222-2-22222222222-22-22-2-2-222-2-22200000000-2-222-2-20000-2-222-2-22200000000000000
χ272222-2-22-2-2222-2-2-2-2222-2-2-2-22222-2-20000000000002-20000000000002i−2i2i−2i2i−2i00000000
χ282222-2-22-2-2222-2-2-2-2222-2-2-2-22222-2-20000000000002-2000000000000−2i2i−2i2i−2i2i00000000
χ292222-2-22-2-2222-2-2-2-2-2-2222-2-2-2-22222000000000000-220000000000000000002-2000000
χ302222-2-22-2-2222-2-2-2-2-2-2222-2-2-2-22222000000000000-22000000000000000000-22000000
χ312222-2-2-122-1-1-1-1-1-1-1-22-22-211-1-111-1-10000−i3−i3i3i322-2-211−i3−i3i3i3-1-111-1-11100−i3i3i3−i300000000
χ322222-2-2-122-1-1-1-1-1-1-1-22-22-211-1-111-1-10000−i3−i3i3i3-2-22211−i3−i3i3i311-1-111-1-100i3−i3−i3i300000000
χ332222-2-2-122-1-1-1-1-1-1-1-22-22-211-1-111-1-10000i3i3−i3−i322-2-211i3i3−i3−i3-1-111-1-11100i3−i3−i3i300000000
χ342222-2-2-122-1-1-1-1-1-1-1-22-22-211-1-111-1-10000i3i3−i3−i3-2-22211i3i3−i3−i311-1-111-1-100−i3i3i3−i300000000
χ352222-2-2-1-2-2-1-1-11111222-2-211-1-1-1-1110000−i3−i3i3i30000-11i3i3−i3−i333−3−3−3−3332i−2i−ii−ii00000000
χ362222-2-2-1-2-2-1-1-11111222-2-211-1-1-1-1110000−i3−i3i3i30000-11i3i3−i3−i3−3−33333−3−3−2i2ii−ii−i00000000
χ372222-2-2-1-2-2-1-1-11111222-2-211-1-1-1-1110000i3i3−i3−i30000-11−i3−i3i3i333−3−3−3−333−2i2ii−ii−i00000000
χ382222-2-2-1-2-2-1-1-11111222-2-211-1-1-1-1110000i3i3−i3−i30000-11−i3−i3i3i3−3−33333−3−32i−2i−ii−ii00000000
χ39444444-244-2-2-2-2-2-2-2-4-44-4-4-2-222-2-2220000000000002200000000000000000000000000
χ40444444-2-4-4-2-2-222224-4-44-4-2-22222-2-2000000000000-2200000000000000000000000000
χ414444-4-4-244-2-2-2-2-2-2-24-4-4-4422222222000000000000-2-200000000000000000000000000
χ424444-4-4-2-4-4-2-2-22222-4-44442222-2-2-2-20000000000002-200000000000000000000000000
χ4344-4-40044i−4i4-4-44i4i−4i−4i00000000000002-22i−2i2-22-20000002i−2i2i−2i0000000000000000000000
χ4444-4-40044i−4i4-4-44i4i−4i−4i0000000000000-22−2i2i-22-22000000−2i2i−2i2i0000000000000000000000
χ4544-4-4004−4i4i4-4-4−4i−4i4i4i00000000000002-2−2i2i2-22-2000000−2i2i−2i2i0000000000000000000000
χ4644-4-4004−4i4i4-4-4−4i−4i4i4i0000000000000-222i−2i-22-220000002i−2i2i−2i0000000000000000000000
χ4744-4-400-24i−4i-222−2i−2i2i2i0000000−2i32i30023−232-22i−2i−1−i31+i3−1+i31−i30000002ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ4844-4-400-24i−4i-222−2i−2i2i2i0000000−2i32i30023−23-22−2i2i1+i3−1−i31−i3−1+i3000000−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ4944-4-400-24i−4i-222−2i−2i2i2i00000002i3−2i300−23232-22i−2i−1+i31−i3−1−i31+i30000002ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ5044-4-400-24i−4i-222−2i−2i2i2i00000002i3−2i300−2323-22−2i2i1−i3−1+i31+i3−1−i3000000−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ5144-4-400-2−4i4i-2222i2i−2i−2i0000000−2i32i300−23232-2−2i2i−1−i31+i3−1+i31−i3000000−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ5244-4-400-2−4i4i-2222i2i−2i−2i0000000−2i32i300−2323-222i−2i1+i3−1−i31−i3−1+i30000002ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ5344-4-400-2−4i4i-2222i2i−2i−2i00000002i3−2i30023−232-2−2i2i−1+i31−i3−1−i31+i3000000−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ5444-4-400-2−4i4i-2222i2i−2i−2i00000002i3−2i30023−23-222i−2i1−i3−1+i31+i3−1−i30000002ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ554-44-44-4400-44-40000000004-4000000000000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i00000000000000
χ564-44-44-4400-44-40000000004-400000000000000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i00000000000000
χ574-44-44-4-2002-2223−2323−2300000-220023−2300000000002i−2i2i−2i000000−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
χ584-44-44-4-2002-2223−2323−2300000-220023−230000000000−2i2i−2i2i000000ζ2−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
χ594-44-44-4-2002-22−2323−232300000-2200−232300000000002i−2i2i−2i000000ζ2+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
χ604-44-44-4-2002-22−2323−232300000-2200−23230000000000−2i2i−2i2i000000−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
χ614-44-4-44400-44-4000000000-44000000000000002i−2i−2i2i0000002i−2i−2i2i2i−2i−2i2i00000000000000
χ624-44-4-44400-44-4000000000-4400000000000000−2i2i2i−2i000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ634-44-4-44-2002-2223−2323−23000002-200−232300000000002i−2i−2i2i000000−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
χ644-44-4-44-2002-2223−2323−23000002-200−23230000000000−2i2i2i−2i000000ζ2−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
χ654-44-4-44-2002-22−2323−2323000002-20023−2300000000002i−2i−2i2i000000ζ2+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
χ664-44-4-44-2002-22−2323−2323000002-20023−230000000000−2i2i2i−2i000000−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
χ678-8-8800800-8-88000000000000000000000000000000000000000000000000000000000
χ688-8-8800-40044-4−4i34i34i3−4i300000000000000000000000000000000000000000000000000000
χ698-8-8800-40044-44i3−4i3−4i34i300000000000000000000000000000000000000000000000000000

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