Finite Group Databasebeta

← Group #11920560

Character table — Group #11920560

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222666666668888888812121212121212121212121212121212161616161616161624242424242424242424242424243636363636367272
order12224444366612121212224444443666121212128888121212122424242424242424366612121212666688121212122424242444888888
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
χ31111111111111111-1-1-1-1111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1ii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-11111i−i-1-1-1-1ii−i−i1-1ii−i−ii−i
χ61111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-11111−ii-1-1-1-1−i−iii1-1−i−iii−ii
χ71111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1ii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1-1-1-1-1i−i1111ii−i−i-11−i−iii−ii
χ81111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1-1-1-1-1−ii1111−i−iii-11ii−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
χ102222222222222222-2-2-2-22222-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-111110011110000-2-2000000
χ1122222222-1-1-1-1-1-1-1-100002222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000220000-1-1-1-100000000
χ1222222222-1-1-1-1-1-1-1-10000222222222222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-10000-2-20000111100000000
χ132222-2-2-2-22222-2-2-2-222-2-222-2-2-1-1-1-11111000022-2-200000000-1-1-1-11111-1-1-1-100111100002-2000000
χ142222-2-2-2-22222-2-2-2-2-2-22222-2-2-1-1-1-11111000022-2-200000000-1-1-1-11111111100-1-1-1-10000-22000000
χ152222-2-2-2-2-1-1-1-11111000022-2-22222-2-2-2-22i2i−2i−2i-1-111−i−i−i−iiiii-1-1-1-1111100002i−2i0000−i−iii00000000
χ162222-2-2-2-2-1-1-1-11111000022-2-22222-2-2-2-2−2i−2i2i2i-1-111iiii−i−i−i−i-1-1-1-111110000−2i2i0000ii−i−i00000000
χ1722-2-222-2-222-2-222-2-22-22-20000-111-111-1-12−22−2000022−2−222−2−2-111-111-1-111-1-10011-1-10000002−22−200
χ1822-2-222-2-222-2-222-2-22-22-20000-111-111-1-1−22−220000−2−222−2−222-111-111-1-111-1-10011-1-1000000−22−2200
χ1922-2-222-2-222-2-222-2-2-22-220000-111-111-1-12−22−2000022−2−222−2−2-111-111-1-1-1-11100-1-111000000−22−2200
χ2022-2-222-2-222-2-222-2-2-22-220000-111-111-1-1−22−220000−2−222−2−222-111-111-1-1-1-11100-1-1110000002−22−200
χ2122-2-2-2-22222-2-2-2-2222-2-220000-111-1-1-111−i2i2i2−i20000−i2−i2i2i2i2i2−i2−i2-111-1-1-11111-1-100-1-111000000−i2i2i2−i200
χ2222-2-2-2-22222-2-2-2-2222-2-220000-111-1-1-111i2−i2−i2i20000i2i2−i2−i2−i2−i2i2i2-111-1-1-11111-1-100-1-111000000i2−i2−i2i200
χ2322-2-2-2-22222-2-2-2-222-222-20000-111-1-1-111−i2i2i2−i20000−i2−i2i2i2i2i2−i2−i2-111-1-1-111-1-1110011-1-1000000i2−i2−i2i200
χ2422-2-2-2-22222-2-2-2-222-222-20000-111-1-1-111i2−i2−i2i20000i2i2−i2−i2−i2−i2i2i2-111-1-1-111-1-1110011-1-1000000−i2i2i2−i200
χ252-22-22i−2i2i−2i2-22-22i−2i2i−2i00002-22i−2i22-2-22i−2i2i−2i00002-22i−2i0000000022-2-22i−2i2i−2i0000000000000000000000
χ262-22-22i−2i2i−2i2-22-22i−2i2i−2i00002-22i−2i-1-111−ii−ii00002-22i−2i00000000-1-111−ii−ii−i3i3−i3i3003−33−3000000000000
χ272-22-22i−2i2i−2i2-22-22i−2i2i−2i00002-22i−2i-1-111−ii−ii00002-22i−2i00000000-1-111−ii−iii3−i3i3−i300−33−33000000000000
χ282-22-22i−2i2i−2i-11-11−ii−ii00002-22i−2i22-2-22i−2i2i−2i0000-11−ii−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13-1-111−ii−ii0000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ292-22-22i−2i2i−2i-11-11−ii−ii00002-22i−2i22-2-22i−2i2i−2i0000-11−iiζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13-1-111−ii−ii0000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ302-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00002-2−2i2i22-2-2−2i2i−2i2i00002-2−2i2i0000000022-2-2−2i2i−2i2i0000000000000000000000
χ312-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00002-2−2i2i-1-111i−ii−i00002-2−2i2i00000000-1-111i−ii−i−i3i3−i3i300−33−33000000000000
χ322-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00002-2−2i2i-1-111i−ii−i00002-2−2i2i00000000-1-111i−ii−ii3−i3i3−i3003−33−3000000000000
χ332-22-2−2i2i−2i2i-11-11i−ii−i00002-2−2i2i22-2-2−2i2i−2i2i0000-11i−iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23-1-111i−ii−i0000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ342-22-2−2i2i−2i2i-11-11i−ii−i00002-2−2i2i22-2-2−2i2i−2i2i0000-11i−i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23-1-111i−ii−i0000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ3533333333333333333333-1-1-1-1000000001111-1-1-1-111111111000000000000-1-10000-1-1-1-1-1-11111-1-1
χ3633333333333333333333-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000001100001111-1-1-1-1-1-111
χ373333333333333333-3-3-3-3-1-1-1-1000000001111-1-1-1-111111111000000000000-1-10000-1-1-1-111-1-1-1-111
χ383333333333333333-3-3-3-3-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000001100001111111111-1-1
χ393333-3-3-3-33333-3-3-3-333-3-3-1-11100000000ii−i−i-1-111iiii−i−i−i−i000000000000−ii0000−i−iii-11ii−i−i−ii
χ403333-3-3-3-33333-3-3-3-333-3-3-1-11100000000−i−iii-1-111−i−i−i−iiiii000000000000i−i0000ii−i−i-11−i−iiii−i
χ413333-3-3-3-33333-3-3-3-3-3-333-1-11100000000ii−i−i-1-111iiii−i−i−i−i000000000000−ii0000−i−iii1-1−i−iiii−i
χ423333-3-3-3-33333-3-3-3-3-3-333-1-11100000000−i−iii-1-111−i−i−i−iiiii000000000000i−i0000ii−i−i1-1ii−i−i−ii
χ4344444444-2-2-2-2-2-2-2-200004444-2-2-2-2-2-2-2-20000-2-2-2-200000000111111110000000000000000000000
χ444444-4-4-4-4-2-2-2-22222000044-4-4-2-2-2-222220000-2-222000000001111-1-1-1-10000000000000000000000
χ4544-4-444-4-444-4-444-4-44-44-400001-1-11-1-11100000000000000001-1-11-1-111-1-11100-1-111000000000000
χ4644-4-444-4-444-4-444-4-4-44-4400001-1-11-1-11100000000000000001-1-11-1-11111-1-10011-1-1000000000000
χ4744-4-444-4-4-2-222-2-22200000000-222-222-2-222−2222−220000−2−222−2−2221-1-11-1-1110000000000000000000000
χ4844-4-444-4-4-2-222-2-22200000000-222-222-2-2−2222−2222000022−2−222−2−21-1-11-1-1110000000000000000000000
χ4944-4-4-4-44444-4-4-4-4444-4-4400001-1-1111-1-100000000000000001-1-1111-1-1-1-1110011-1-1000000000000
χ5044-4-4-4-44444-4-4-4-444-444-400001-1-1111-1-100000000000000001-1-1111-1-111-1-100-1-111000000000000
χ5144-4-4-4-444-2-22222-2-200000000-222-2-2-222−2i22i22i2−2i20000i2i2−i2−i2−i2−i2i2i21-1-1111-1-10000000000000000000000
χ5244-4-4-4-444-2-22222-2-200000000-222-2-2-2222i2−2i2−2i22i20000−i2−i2i2i2i2i2−i2−i21-1-1111-1-10000000000000000000000
χ534-44-44i−4i4i−4i-22-22−2i2i−2i2i00004-44i−4i-2-222−2i2i−2i2i0000-22−2i2i0000000011-1-1i−ii−i0000000000000000000000
χ544-44-4−4i4i−4i4i-22-222i−2i2i−2i00004-4−4i4i-2-2222i−2i2i−2i0000-222i−2i0000000011-1-1−ii−ii0000000000000000000000
χ554-4-444i−4i−4i4i4-4-444i−4i−4i4i000000001-11-1−iii−i00000000000000001-11-1−iii−i−i3i3i3−i3003−3−33000000000000
χ564-4-444i−4i−4i4i4-4-444i−4i−4i4i000000001-11-1−iii−i00000000000000001-11-1−iii−ii3−i3−i3i300−333−3000000000000
χ574-4-444i−4i−4i4i4-4-444i−4i−4i4i00000000-22-222i−2i−2i2i0000000000000000-22-222i−2i−2i2i0000000000000000000000
χ584-4-444i−4i−4i4i-222-2−2i2i2i−2i00000000-22-222i−2i−2i2i00000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ221-11-1−iii−i0000000000000000000000
χ594-4-444i−4i−4i4i-222-2−2i2i2i−2i00000000-22-222i−2i−2i2i00000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ221-11-1−iii−i0000000000000000000000
χ604-4-44−4i4i4i−4i4-4-44−4i4i4i−4i000000001-11-1i−i−ii00000000000000001-11-1i−i−ii−i3i3i3−i300−333−3000000000000
χ614-4-44−4i4i4i−4i4-4-44−4i4i4i−4i000000001-11-1i−i−ii00000000000000001-11-1i−i−iii3−i3−i3i3003−3−33000000000000
χ624-4-44−4i4i4i−4i4-4-44−4i4i4i−4i00000000-22-22−2i2i2i−2i0000000000000000-22-22−2i2i2i−2i0000000000000000000000
χ634-4-44−4i4i4i−4i-222-22i−2i−2i2i00000000-22-22−2i2i2i−2i00000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ221-11-1i−i−ii0000000000000000000000
χ644-4-44−4i4i4i−4i-222-22i−2i−2i2i00000000-22-22−2i2i2i−2i00000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ221-11-1i−i−ii0000000000000000000000
χ6566666666-3-3-3-3-3-3-3-30000-2-2-2-20000000022221111-1-1-1-1-1-1-1-1000000000000-2-20000111100000000
χ6666666666-3-3-3-3-3-3-3-30000-2-2-2-200000000-2-2-2-2111111111111000000000000220000-1-1-1-100000000
χ676666-6-6-6-6-3-3-3-333330000-2-222000000002i2i−2i−2i11-1-1−i−i−i−iiiii000000000000−2i2i0000ii−i−i00000000
χ686666-6-6-6-6-3-3-3-333330000-2-22200000000−2i−2i2i2i11-1-1iiii−i−i−i−i0000000000002i−2i0000−i−iii00000000
χ696-66-66i−6i6i−6i6-66-66i−6i6i−6i0000-22−2i2i000000000000-22−2i2i00000000000000000000000000000000000000
χ706-66-66i−6i6i−6i-33-33−3i3i−3i3i0000-22−2i2i0000000000001-1i−i−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ716-66-66i−6i6i−6i-33-33−3i3i−3i3i0000-22−2i2i0000000000001-1i−iζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ726-66-6−6i6i−6i6i6-66-6−6i6i−6i6i0000-222i−2i000000000000-222i−2i00000000000000000000000000000000000000
χ736-66-6−6i6i−6i6i-33-333i−3i3i−3i0000-222i−2i0000000000001-1−iiζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ746-66-6−6i6i−6i6i-33-333i−3i3i−3i0000-222i−2i0000000000001-1−ii−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ7588-8-888-8-8-4-444-4-444000000002-2-22-2-2220000000000000000-111-111-1-10000000000000000000000
χ7688-8-8-8-888-4-44444-4-4000000002-2-2222-2-20000000000000000-111-1-1-1110000000000000000000000
χ778-8-888i−8i−8i8i-444-4−4i4i4i−4i000000002-22-2−2i2i2i−2i0000000000000000-11-11i−i−ii0000000000000000000000
χ788-8-88−8i8i8i−8i-444-44i−4i−4i4i000000002-22-22i−2i−2i2i0000000000000000-11-11−iii−i0000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.