Finite Group Databasebeta

← Group #10698401

Character table — Group #10698401

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888888888888888881616161616164848484848484848
order12222234466612121212224446666121212124444444461212121212121212121212121212121212882424242444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ4111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ511111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-111-1-1-1
χ611111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111
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
χ92222222222222222-2-22-2-222-2-222-2-200000000-2-2000000000000000000000000200-200
χ102222222222222222-2-22-2-222-2-222-2-200000000-2-2000000000000000000000000-200200
χ112222222-2-2222-2-2-2-222-2-2-22222-2-2-2-2000000002-200000000000000000000000002-2000
χ122222222-2-2222-2-2-2-222-2-2-22222-2-2-2-2000000002-20000000000000000000000000-22000
χ132222222-2-2222-2-2-2-2-2-2-22222-2-2-2-22222-2-20000-222222-2-2-2-20000000000000000000000
χ142222222-2-2222-2-2-2-2-2-2-22222-2-2-2-222-2-2220000-22-2-2-2-222220000000000000000000000
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
χ19222222-1-2-2-1-1-11111-2-2-222-1-11111-1-122-2-200001-1-1-1-1-111113333−3−3−3−30033−3−300000000
χ20222222-1-2-2-1-1-11111-2-2-222-1-11111-1-122-2-200001-1-1-1-1-11111−3−3−3−3333300−3−33300000000
χ21222222-1-2-2-1-1-11111-2-2-222-1-11111-1-1-2-22200001-11111-1-1-1-13333−3−3−3−300−3−33300000000
χ22222222-1-2-2-1-1-11111-2-2-222-1-11111-1-1-2-22200001-11111-1-1-1-1−3−3−3−333330033−3−300000000
χ232222-2-222222222222-2-2-22-2-2-2-2-2-2-2-200002i2i−2i−2i22000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ242222-2-222222222222-2-2-22-2-2-2-2-2-2-2-20000−2i−2i2i2i2200000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ252222-2-22222222222-22-22-2-2-222-2-22200000000-2-200000000000000000000000000002i−2i
χ262222-2-22222222222-22-22-2-2-222-2-22200000000-2-20000000000000000000000000000−2i2i
χ272222-2-22-2-2222-2-2-2-22-222-2-2-2-2-22222000000002-200000000000000000000002-2000000
χ282222-2-22-2-2222-2-2-2-22-222-2-2-2-2-22222000000002-20000000000000000000000-22000000
χ292222-2-22-2-2222-2-2-2-2-222-22-2-22222-2-200000000-2200000000000000002i−2i2i−2i2i−2i00000000
χ302222-2-22-2-2222-2-2-2-2-222-22-2-22222-2-200000000-220000000000000000−2i2i−2i2i−2i2i00000000
χ312222-2-2-122-1-1-1-1-1-1-12-2-2-221111111100002i2i−2i−2i-1-133−3−333−3−3−i−iii−i−iii00−i3i3i3−i300000000
χ322222-2-2-122-1-1-1-1-1-1-12-2-2-221111111100002i2i−2i−2i-1-1−3−333−3−333−i−iii−i−iii00i3−i3−i3i300000000
χ332222-2-2-122-1-1-1-1-1-1-12-2-2-22111111110000−2i−2i2i2i-1-133−3−333−3−3ii−i−iii−i−i00i3−i3−i3i300000000
χ342222-2-2-122-1-1-1-1-1-1-12-2-2-22111111110000−2i−2i2i2i-1-1−3−333−3−333ii−i−iii−i−i00−i3i3i3−i300000000
χ352222-2-2-1-2-2-1-1-11111-222-2211-1-1-1-111000000001-133−3−3−3−333−i3−i3i3i3i3i3−i3−i3−2i2ii−ii−i00000000
χ362222-2-2-1-2-2-1-1-11111-222-2211-1-1-1-111000000001-133−3−3−3−333i3i3−i3−i3−i3−i3i3i32i−2i−ii−ii00000000
χ372222-2-2-1-2-2-1-1-11111-222-2211-1-1-1-111000000001-1−3−33333−3−3−i3−i3i3i3i3i3−i3−i32i−2i−ii−ii00000000
χ382222-2-2-1-2-2-1-1-11111-222-2211-1-1-1-111000000001-1−3−33333−3−3i3i3−i3−i3−i3−i3i3i3−2i2ii−ii−i00000000
χ39444444-244-2-2-2-2-2-2-2-4-44-4-4-2-222-2-2220000000022000000000000000000000000000000
χ40444444-2-4-4-2-2-2222244-4-4-4-2-2-2-2222200000000-22000000000000000000000000000000
χ414444-4-4-244-2-2-2-2-2-2-2-44-44-422-2-222-2-20000000022000000000000000000000000000000
χ424444-4-4-2-4-4-2-2-222224-444-42222-2-2-2-200000000-22000000000000000000000000000000
χ4344-4-44-44004-4-40000000004-400000000002-22-200000000002-22-22-22-200000000000000
χ4444-4-44-44004-4-40000000004-40000000000-22-220000000000-22-22-22-2200000000000000
χ4544-4-44-4-200-2222323−23−2300000-220023−230000002-22-20000000000−1+31−3−1+31−3−1−31+3−1−31+300000000000000
χ4644-4-44-4-200-2222323−23−2300000-220023−23000000-22-2200000000001−3−1+31−3−1+31+3−1−31+3−1−300000000000000
χ4744-4-44-4-200-222−23−23232300000-2200−23230000002-22-20000000000−1−31+3−1−31+3−1+31−3−1+31−300000000000000
χ4844-4-44-4-200-222−23−23232300000-2200−2323000000-22-2200000000001+3−1−31+3−1−31−3−1+31−3−1+300000000000000
χ4944-4-4-444004-4-4000000000-4400000000002i−2i−2i2i00000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ5044-4-4-444004-4-4000000000-440000000000−2i2i2i−2i0000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ5144-4-4-44-200-2222323−23−23000002-200−23230000002i−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
χ5244-4-4-44-200-2222323−23−23000002-200−2323000000−2i2i2i−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
χ5344-4-4-44-200-222−23−232323000002-20023−230000002i−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
χ5444-4-4-44-200-222−23−232323000002-20023−23000000−2i2i2i−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
χ554-44-40044i−4i-44-44i−4i4i−4i00000000000002i−2i2-20000002i−2i2i−2i2-22-20000000000000000000000
χ564-44-40044i−4i-44-44i−4i4i−4i0000000000000−2i2i-22000000−2i2i−2i2i-22-220000000000000000000000
χ574-44-4004−4i4i-44-4−4i4i−4i4i00000000000002i−2i-220000002i−2i2i−2i-22-220000000000000000000000
χ584-44-4004−4i4i-44-4−4i4i−4i4i0000000000000−2i2i2-2000000−2i2i−2i2i2-22-20000000000000000000000
χ594-44-400-24i−4i2-22−2i2i−2i2i0000000−2i32i30023−232i−2i2-2000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−1−31+3−1+31−30000000000000000000000
χ604-44-400-24i−4i2-22−2i2i−2i2i0000000−2i32i30023−23−2i2i-22000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ111+3−1−31−3−1+30000000000000000000000
χ614-44-400-24i−4i2-22−2i2i−2i2i00000002i3−2i300−23232i−2i2-2000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−1+31−3−1−31+30000000000000000000000
χ624-44-400-24i−4i2-22−2i2i−2i2i00000002i3−2i300−2323−2i2i-22000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ111−3−1+31+3−1−30000000000000000000000
χ634-44-400-2−4i4i2-222i−2i2i−2i0000000−2i32i300−23232i−2i-22000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ111−3−1+31+3−1−30000000000000000000000
χ644-44-400-2−4i4i2-222i−2i2i−2i0000000−2i32i300−2323−2i2i2-2000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−1+31−3−1−31+30000000000000000000000
χ654-44-400-2−4i4i2-222i−2i2i−2i00000002i3−2i30023−232i−2i-22000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ111+3−1−31−3−1+30000000000000000000000
χ664-44-400-2−4i4i2-222i−2i2i−2i00000002i3−2i30023−23−2i2i2-2000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−1−31+3−1+31−30000000000000000000000
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.