Finite Group Databasebeta

← Group #11920717

Character table — Group #11920717

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222666666668888888812121212121212121212121212121212161616161616161624242424242424242424242424243636363636367272
order122244443666121212122222444436661212121244446612121212121212121212366612121212666688121212122424242424444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-111-1-1-1-1-1-1
χ31111111111111111-1-11111-1-111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1ii−i−i-1-111iiii−i−i−i−i1111-1-1-1-11111i−i-1-1-1-1ii−i−i-11ii−i−ii−i
χ61111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1−i−iii-1-111−i−i−i−iiiii1111-1-1-1-11111−ii-1-1-1-1−i−iii-11−i−iii−ii
χ71111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i-1-111iiii−i−i−i−i1111-1-1-1-1-1-1-1-1i−i1111ii−i−i1-1−i−iii−ii
χ81111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iii-1-111−i−i−i−iiiii1111-1-1-1-1-1-1-1-1−ii1111−i−iii1-1ii−i−ii−i
χ9222222222222222222222222-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1-1-1-1-100-1-1-1-1000022000000
χ102222222222222222-2-22222-2-2-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-111110011110000-2-2000000
χ1122222222-1-1-1-1-1-1-1-100222200222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000220000-1-1-1-100000000
χ1222222222-1-1-1-1-1-1-1-10022220022222222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-10000-2-20000111100000000
χ132222-2-2-2-22222-2-2-2-222-2-222-2-2-1-1-1-111110000-2-22200000000-1-1-1-11111-1-1-1-10011110000-22000000
χ142222-2-2-2-22222-2-2-2-2-2-2-2-22222-1-1-1-111110000-2-22200000000-1-1-1-11111111100-1-1-1-100002-2000000
χ152222-2-2-2-2-1-1-1-1111100-2-222002222-2-2-2-22i2i−2i−2i11-1-1−i−i−i−iiiii-1-1-1-1111100002i−2i0000−i−iii00000000
χ162222-2-2-2-2-1-1-1-1111100-2-222002222-2-2-2-2−2i−2i2i2i11-1-1iiii−i−i−i−i-1-1-1-111110000−2i2i0000ii−i−i00000000
χ1722-2-22i−2i2i−2i22-2-22i−2i2i−2i2-200002i−2i-11-11ii−i−i1+i−1−i1−i−1+i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i-11-11ii−i−i11-1-100ii−i−i0000001+i−1−i1−i−1+i00
χ1822-2-22i−2i2i−2i22-2-22i−2i2i−2i2-200002i−2i-11-11ii−i−i−1−i1+i−1+i1−i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i-11-11ii−i−i11-1-100ii−i−i000000−1−i1+i−1+i1−i00
χ1922-2-22i−2i2i−2i22-2-22i−2i2i−2i-220000−2i2i-11-11ii−i−i1+i−1−i1−i−1+i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i-11-11ii−i−i-1-11100−i−iii000000−1−i1+i−1+i1−i00
χ2022-2-22i−2i2i−2i22-2-22i−2i2i−2i-220000−2i2i-11-11ii−i−i−1−i1+i−1+i1−i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i-11-11ii−i−i-1-11100−i−iii0000001+i−1−i1−i−1+i00
χ2122-2-2−2i2i−2i2i22-2-2−2i2i−2i2i2-20000−2i2i-11-11−i−iii1−i−1+i1+i−1−i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i-11-11−i−iii11-1-100−i−iii0000001−i−1+i1+i−1−i00
χ2222-2-2−2i2i−2i2i22-2-2−2i2i−2i2i2-20000−2i2i-11-11−i−iii−1+i1−i−1−i1+i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i-11-11−i−iii11-1-100−i−iii000000−1+i1−i−1−i1+i00
χ2322-2-2−2i2i−2i2i22-2-2−2i2i−2i2i-2200002i−2i-11-11−i−iii1−i−1+i1+i−1−i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i-11-11−i−iii-1-11100ii−i−i000000−1+i1−i−1−i1+i00
χ2422-2-2−2i2i−2i2i22-2-2−2i2i−2i2i-2200002i−2i-11-11−i−iii−1+i1−i−1−i1+i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i-11-11−i−iii-1-11100ii−i−i0000001−i−1+i1+i−1−i00
χ252-2-2222-2-22-2-22-2-222002-22-2002-2-222-22-20000-222-2000000002-2-222-22-20000000000000000000000
χ262-2-2222-2-22-2-22-2-222002-22-200-111-1-11-110000-222-200000000-111-1-11-11−i3i3−i3i300−i3i3−i3i3000000000000
χ272-2-2222-2-22-2-22-2-222002-22-200-111-1-11-110000-222-200000000-111-1-11-11i3−i3i3−i300i3−i3i3−i3000000000000
χ282-2-2222-2-2-111-111-1-1002-22-2002-2-222-22-200001-1-11−i3i3−i3i3−i3i3−i3i3-111-1-11-110000000000−i3i3−i3i300000000
χ292-2-2222-2-2-111-111-1-1002-22-2002-2-222-22-200001-1-11i3−i3i3−i3i3−i3i3−i3-111-1-11-110000000000i3−i3i3−i300000000
χ302-2-22-2-2222-2-2222-2-200-222-2002-2-22-22-2200002-22-2000000002-2-22-22-220000000000000000000000
χ312-2-22-2-2222-2-2222-2-200-222-200-111-11-11-100002-22-200000000-111-11-11-1−i3i3−i3i300i3−i3i3−i3000000000000
χ322-2-22-2-2222-2-2222-2-200-222-200-111-11-11-100002-22-200000000-111-11-11-1i3−i3i3−i300−i3i3−i3i3000000000000
χ332-2-22-2-222-111-1-1-11100-222-2002-2-22-22-220000-11-113−33−3−33−33-111-11-11-100000000003−3−3300000000
χ342-2-22-2-222-111-1-1-11100-222-2002-2-22-22-220000-11-11−33−333−33−3-111-11-11-10000000000−333−300000000
χ35333333333333333333-1-1-1-133000000001111-1-1-1-111111111000000000000-1-10000-1-1-1-1-1-11111-1-1
χ36333333333333333333-1-1-1-13300000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000001100001111-1-1-1-1-1-111
χ373333333333333333-3-3-1-1-1-1-3-3000000001111-1-1-1-111111111000000000000-1-10000-1-1-1-111-1-1-1-111
χ383333333333333333-3-3-1-1-1-1-3-300000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000001100001111111111-1-1
χ393333-3-3-3-33333-3-3-3-33311-1-1-3-300000000ii−i−i11-1-1iiii−i−i−i−i000000000000−ii0000−i−iii1-1ii−i−i−ii
χ403333-3-3-3-33333-3-3-3-33311-1-1-3-300000000−i−iii11-1-1−i−i−i−iiiii000000000000i−i0000ii−i−i1-1−i−iiii−i
χ413333-3-3-3-33333-3-3-3-3-3-311-1-13300000000ii−i−i11-1-1iiii−i−i−i−i000000000000−ii0000−i−iii-11−i−iiii−i
χ423333-3-3-3-33333-3-3-3-3-3-311-1-13300000000−i−iii11-1-1−i−i−i−iiiii000000000000i−i0000ii−i−i-11ii−i−i−ii
χ4344444444-2-2-2-2-2-2-2-200444400-2-2-2-2-2-2-2-20000-2-2-2-200000000111111110000000000000000000000
χ444444-4-4-4-4-2-2-2-2222200-4-44400-2-2-2-22222000022-2-2000000001111-1-1-1-10000000000000000000000
χ4544-4-44i−4i4i−4i44-4-44i−4i4i−4i4-400004i−4i1-11-1−i−iii00000000000000001-11-1−i−iii-1-11100−i−iii000000000000
χ4644-4-44i−4i4i−4i44-4-44i−4i4i−4i-440000−4i4i1-11-1−i−iii00000000000000001-11-1−i−iii11-1-100ii−i−i000000000000
χ4744-4-44i−4i4i−4i-2-222−2i2i−2i2i00000000-22-222i2i−2i−2i2+2i−2−2i2−2i−2+2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1-11-1−i−iii0000000000000000000000
χ4844-4-44i−4i4i−4i-2-222−2i2i−2i2i00000000-22-222i2i−2i−2i−2−2i2+2i−2+2i2−2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i1-11-1−i−iii0000000000000000000000
χ4944-4-4−4i4i−4i4i44-4-4−4i4i−4i4i4-40000−4i4i1-11-1ii−i−i00000000000000001-11-1ii−i−i-1-11100ii−i−i000000000000
χ5044-4-4−4i4i−4i4i44-4-4−4i4i−4i4i-4400004i−4i1-11-1ii−i−i00000000000000001-11-1ii−i−i11-1-100−i−iii000000000000
χ5144-4-4−4i4i−4i4i-2-2222i−2i2i−2i00000000-22-22−2i−2i2i2i2−2i−2+2i2+2i−2−2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1-11-1ii−i−i0000000000000000000000
χ5244-4-4−4i4i−4i4i-2-2222i−2i2i−2i00000000-22-22−2i−2i2i2i−2+2i2−2i−2−2i2+2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i1-11-1ii−i−i0000000000000000000000
χ534-44-44i−4i−4i4i4-44-4−4i4i4i−4i0000000011-1-1−iii−i000000000000000011-1-1−iii−i−i3i3i3−i3003−3−33000000000000
χ544-44-44i−4i−4i4i4-44-4−4i4i4i−4i0000000011-1-1−iii−i000000000000000011-1-1−iii−ii3−i3−i3i300−333−3000000000000
χ554-44-44i−4i−4i4i4-44-4−4i4i4i−4i00000000-2-2222i−2i−2i2i0000000000000000-2-2222i−2i−2i2i0000000000000000000000
χ564-44-44i−4i−4i4i-22-222i−2i−2i2i00000000-2-2222i−2i−2i2i00000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1111-1-1−iii−i0000000000000000000000
χ574-44-44i−4i−4i4i-22-222i−2i−2i2i00000000-2-2222i−2i−2i2i00000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1111-1-1−iii−i0000000000000000000000
χ584-44-4−4i4i4i−4i4-44-44i−4i−4i4i0000000011-1-1i−i−ii000000000000000011-1-1i−i−ii−i3i3i3−i300−333−3000000000000
χ594-44-4−4i4i4i−4i4-44-44i−4i−4i4i0000000011-1-1i−i−ii000000000000000011-1-1i−i−iii3−i3−i3i3003−3−33000000000000
χ604-44-4−4i4i4i−4i4-44-44i−4i−4i4i00000000-2-222−2i2i2i−2i0000000000000000-2-222−2i2i2i−2i0000000000000000000000
χ614-44-4−4i4i4i−4i-22-22−2i2i2i−2i00000000-2-222−2i2i2i−2i00000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1111-1-1i−i−ii0000000000000000000000
χ624-44-4−4i4i4i−4i-22-22−2i2i2i−2i00000000-2-222−2i2i2i−2i00000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1111-1-1i−i−ii0000000000000000000000
χ634-4-4444-4-4-222-222-2-2004-44-400-222-2-22-2200002-2-22000000001-1-111-11-10000000000000000000000
χ644-4-44-4-444-222-2-2-22200-444-400-222-22-22-20000-22-22000000001-1-11-11-110000000000000000000000
χ6566666666-3-3-3-3-3-3-3-300-2-2-2-2000000000022221111-1-1-1-1-1-1-1-1000000000000-2-20000111100000000
χ6666666666-3-3-3-3-3-3-3-300-2-2-2-20000000000-2-2-2-2111111111111000000000000220000-1-1-1-100000000
χ676666-6-6-6-6-3-3-3-333330022-2-200000000002i2i−2i−2i-1-111−i−i−i−iiiii000000000000−2i2i0000ii−i−i00000000
χ686666-6-6-6-6-3-3-3-333330022-2-20000000000−2i−2i2i2i-1-111iiii−i−i−i−i0000000000002i−2i0000−i−iii00000000
χ696-6-6666-6-66-6-66-6-66600-22-22000000000000002-2-2200000000000000000000000000000000000000
χ706-6-6666-6-6-333-333-3-300-22-2200000000000000-111-1−i3i3−i3i3−i3i3−i3i3000000000000000000i3−i3i3−i300000000
χ716-6-6666-6-6-333-333-3-300-22-2200000000000000-111-1i3−i3i3−i3i3−i3i3−i3000000000000000000−i3i3−i3i300000000
χ726-6-66-6-6666-6-6666-6-6002-2-2200000000000000-22-2200000000000000000000000000000000000000
χ736-6-66-6-666-333-3-3-333002-2-22000000000000001-11-13−33−3−33−33000000000000000000−333−300000000
χ746-6-66-6-666-333-3-3-333002-2-22000000000000001-11-1−33−333−33−30000000000000000003−3−3300000000
χ7588-8-88i−8i8i−8i-4-444−4i4i−4i4i000000002-22-2−2i−2i2i2i0000000000000000-11-11ii−i−i0000000000000000000000
χ7688-8-8−8i8i−8i8i-4-4444i−4i4i−4i000000002-22-22i2i−2i−2i0000000000000000-11-11−i−iii0000000000000000000000
χ778-88-88i−8i−8i8i-44-444i−4i−4i4i0000000022-2-2−2i2i2i−2i0000000000000000-1-111i−i−ii0000000000000000000000
χ788-88-8−8i8i8i−8i-44-44−4i4i4i−4i0000000022-2-22i−2i−2i2i0000000000000000-1-111−iii−i0000000000000000000000

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