Finite Group Databasebeta

← Group #13166069

Character table — Group #13166069

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size1223334666666691212121212121227272732363636363636363654646464647272727272727272288
order1332443466121212122612121212121224432244888843333661212242424246
χ1111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11
χ311111111111111-11111111-1-1-111-11-111-1-1-111111-11-111-1-1-1
χ411111111111111-11111111-1-1-11-11-11-1-111-11111-11-11-1-111-1
χ52222222222222222222222222-1000000002-1-1-1-100000000-1
χ622222222222222-22222222-2-2-2-100000000-2-1-1-1-1000000001
χ722-1222-122-122-1-10-12-1-1-1-1-100020202002202-1-1-10-10-100-1-10
χ822-1222-122-122-1-10-12-1-1-1-1-100020-20-200-2-202-1-1-1010100110
χ92-12222-12-12-1-1220-1-12-1-1-1-10002202022000-12-1-1-10-10-1-1000
χ102-12222-12-12-1-1220-1-12-1-1-1-10002-20-20-2-2000-12-1-1101011000
χ113333-1-13-133-1-1-1-133-1-1-1-1-1-13-1-101111-1-1-1-1-100001111-1-1-1-10
χ123333-1-13-133-1-1-1-133-1-1-1-1-1-13-1-10-1-1-1-11111-10000-1-1-1-111110
χ133333-1-13-133-1-1-1-1-33-1-1-1-1-1-1-31101-11-1-1-111100001-11-1-1-1110
χ143333-1-13-133-1-1-1-1-33-1-1-1-1-1-1-3110-11-1111-1-110000-11-1111-1-10
χ15333-1−1+2i−1−2i31-1-1−1+2i−1−2i−1+2i−1−2i3-11111−1+2i−1−2i-1−1+2i−1−2i011-1-1i−ii−i1000011-1-1i−ii−i0
χ16333-1−1+2i−1−2i31-1-1−1+2i−1−2i−1+2i−1−2i3-11111−1+2i−1−2i-1−1+2i−1−2i0-1-111−ii−ii10000-1-111−ii−ii0
χ17333-1−1+2i−1−2i31-1-1−1+2i−1−2i−1+2i−1−2i-3-11111−1+2i−1−2i11−2i1+2i01-1-11i−i−ii-100001-1-11i−i−ii0
χ18333-1−1+2i−1−2i31-1-1−1+2i−1−2i−1+2i−1−2i-3-11111−1+2i−1−2i11−2i1+2i0-111-1−iii−i-10000-111-1−iii−i0
χ19333-1−1−2i−1+2i31-1-1−1−2i−1+2i−1−2i−1+2i3-11111−1−2i−1+2i-1−1−2i−1+2i011-1-1−ii−ii1000011-1-1−ii−ii0
χ20333-1−1−2i−1+2i31-1-1−1−2i−1+2i−1−2i−1+2i3-11111−1−2i−1+2i-1−1−2i−1+2i0-1-111i−ii−i10000-1-111i−ii−i0
χ21333-1−1−2i−1+2i31-1-1−1−2i−1+2i−1−2i−1+2i-3-11111−1−2i−1+2i11+2i1−2i01-1-11−iii−i-100001-1-11−iii−i0
χ22333-1−1−2i−1+2i31-1-1−1−2i−1+2i−1−2i−1+2i-3-11111−1−2i−1+2i11+2i1−2i0-111-1i−i−ii-10000-111-1i−i−ii0
χ2344-2444-244-244-2-20-24-2-2-2-2-2000-2000000000-2111000000000
χ244-24444-24-24-2-2440-2-24-2-2-2-2000-20000000001-211000000000
χ254-2-244414-2-2-2-2-2-201-2-211110004000000000-2-211000000000
χ264-2-244414-2-2-2-2-2-201-2-21111000-200000000011−1−3i32−1+3i32000000000
χ274-2-244414-2-2-2-2-2-201-2-21111000-200000000011−1+3i32−1−3i32000000000
χ28666-2226-2-2-222226-2-2-2-2-222-222000000000-20000000000000
χ29666-2226-2-2-22222-6-2-2-2-2-2222-2-200000000020000000000000
χ3066-36-2-2-3-26-3-2-2110-3-2111110000020200-2-2000000-10-100110
χ3166-36-2-2-3-26-3-2-2110-3-21111100000-20-2002200000010100-1-10
χ3266-3-2−2+4i−2−4i-32-21−2+4i−2−4i1−2i1+2i012-1-1-11−2i1+2i0000020-2002i−2i000000-10100−ii0
χ3366-3-2−2+4i−2−4i-32-21−2+4i−2−4i1−2i1+2i012-1-1-11−2i1+2i00000-20200−2i2i00000010-100i−i0
χ3466-3-2−2−4i−2+4i-32-21−2−4i−2+4i1+2i1−2i012-1-1-11+2i1−2i0000020-200−2i2i000000-10100i−i0
χ3566-3-2−2−4i−2+4i-32-21−2−4i−2+4i1+2i1−2i012-1-1-11+2i1−2i00000-202002i−2i00000010-100−ii0
χ366-366-2-2-3-2-3611-2-20-31-2111100002020-2-20000000-10-1011000
χ376-366-2-2-3-2-3611-2-20-31-211110000-20-202200000001010-1-1000
χ386-36-2−2+4i−2−4i-321-21−2i1+2i−2+4i−2−4i01-12-1-11−2i1+2i000020-202i−2i0000000-1010−ii000
χ396-36-2−2+4i−2−4i-321-21−2i1+2i−2+4i−2−4i01-12-1-11−2i1+2i0000-2020−2i2i000000010-10i−i000
χ406-36-2−2−4i−2+4i-321-21+2i1−2i−2−4i−2+4i01-12-1-11+2i1−2i000020-20−2i2i0000000-1010i−i000
χ416-36-2−2−4i−2+4i-321-21+2i1−2i−2−4i−2+4i01-12-1-11+2i1−2i0000-20202i−2i000000010-10−ii000
χ421212-6-444-6-4-4244-2-202-4222-2-200000000000000000000000000
χ4312-612-444-6-42-4-2-244022-422-2-200000000000000000000000000
χ4412-6-612-4-43-4-6-622220322-1-1-1-100000000000000000000000000
χ4512-6-6-4443-422-2-2-2-20-122−1+6i−1−6i1100000000000000000000000000
χ4612-6-6-4443-422-2-2-2-20-122−1−6i−1+6i1100000000000000000000000000
χ4712-6-6-4−4+8i−4−8i34222−4i2+4i2−4i2+4i0-1-2-211−1+2i−1−2i00000000000000000000000000
χ4812-6-6-4−4−8i−4+8i34222+4i2−4i2+4i2−4i0-1-2-211−1−2i−1+2i00000000000000000000000000

Here i is the imaginary unit (i² = −1).