Finite Group Databasebeta

← Group #13180804

Character table — Group #13180804

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size11222222233444446666666888888888888121212121616161616161616161616161818242424242424242424242424242436363636363672727272108108108108
order1223366664436666444121212123336666666661212121233366666666622121212121212121212121212121224668861224242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1
χ3111111111-1-1111111-11-1-1-1-11111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ4111111111-1-1111111-11-1-1-1-11111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511-111-1-111111-1-1-11-1-1111-1-1111-1-1-1-1-1-11111-1-11111111-1-1-1-1-1-11-11-1111111-1-1-1-1-1-11-11-11-11-11-1-111-1
χ611-111-1-111111-1-1-11-1-1111-1-1111-1-1-1-1-1-11111-1-11111111-1-1-1-1-1-11-11-1111111-1-1-1-1-1-1-111-1-11-11-111-1-11
χ711-111-1-111-1-11-1-1-11-111-1-111111-1-1-1-1-1-11111-1-11111111-1-1-1-1-1-1-111-1-1-1-1-1-1-11111111-1-111-11-11-11-1-11
χ811-111-1-111-1-11-1-1-11-111-1-111111-1-1-1-1-1-11111-1-11111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1111111-11-11-11-11-11-111-1
χ922222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100220000000000
χ10222222222-2-2222222-22-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-22211111111111100-2-20000000000
χ112222-1222-100-1-1-1-1-1202000022222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-100-1-1000000000000220022-1-1-1-10000
χ122222-1222-100-1-1-1-1-1202000022222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-100-1-1000000000000-2-200-2-211110000
χ13222-12-1-1-1222-12-1-1-1222-1-1-1-12-1-122-1-1-1-12-1-1-1-1222-1-12-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-100-1-10000000000
χ14222-12-1-1-1222-12-1-1-1222-1-1-1-1-12-1-1-122-1-1-12-1-1-122-12-1-12-1-1-122-1-122-1-1-1-122-1-1-1-122-1-100-1-10000000000
χ15222-12-1-1-1222-12-1-1-1222-1-1-1-1-1-12-1-1-1-122-1-12-1-122-1-12-1-12-1-1-1-12222-1-1-1-1-1-122-1-1-1-12200-1-10000000000
χ16222-12-1-1-12-2-2-12-1-1-12-2211112-1-122-1-1-1-12-1-1-1-1222-1-12-1-122-1-1-1-1-2-2-1-1-2-21111-2-2111100110000000000
χ17222-12-1-1-12-2-2-12-1-1-12-221111-12-1-1-122-1-1-12-1-1-122-12-1-12-1-1-122-1-1-2-2-1-111-2-21111-2-21100110000000000
χ18222-12-1-1-12-2-2-12-1-1-12-221111-1-12-1-1-1-122-1-12-1-122-1-12-1-12-1-1-1-122-2-2-1-11111-2-21111-2-200110000000000
χ1922-222-2-222222-2-2-22-2-2222-2-2-1-1-1111111-1-1-12-2-22-1-1-1-1-1-11111112-22-2-1-1-1-1-1-1111111002-20000000000
χ2022-222-2-222-2-22-2-2-22-222-2-222-1-1-1111111-1-1-12-2-22-1-1-1-1-1-1111111-222-2111111-1-1-1-1-1-100-220000000000
χ2122-22-1-2-22-100-1111-1-2020000222-2-2-2-2-2-22222-21-1-1-1-1-1-1-111111100-110000000000002-2002-2-11-110000
χ2222-22-1-2-22-100-1111-1-2020000222-2-2-2-2-2-22222-21-1-1-1-1-1-1-111111100-11000000000000-2200-221-11-10000
χ2322-2-1211-1222-1-211-1-2-22-1-1112-1-1-2-211112-1-1-11-222-1-12-1-1-2-211112-2-1122-1-1-1-1-2-2111100-110000000000
χ2422-2-1211-1222-1-211-1-2-22-1-111-12-111-2-211-12-1-11-22-12-1-12-111-2-2112-2-11-1-122-1-111-2-21100-110000000000
χ2522-2-1211-1222-1-211-1-2-22-1-111-1-121111-2-2-1-12-11-22-1-12-1-121111-2-22-2-11-1-1-1-1221111-2-200-110000000000
χ2622-2-1211-12-2-2-1-211-1-22211-1-12-1-1-2-211112-1-1-11-222-1-12-1-1-2-21111-22-11-2-2111122-1-1-1-1001-10000000000
χ2722-2-1211-12-2-2-1-211-1-22211-1-1-12-111-2-211-12-1-11-22-12-1-12-111-2-211-22-1111-2-211-1-122-1-1001-10000000000
χ2822-2-1211-12-2-2-1-211-1-22211-1-1-1-121111-2-2-1-12-11-22-1-12-1-121111-2-2-22-111111-2-2-1-1-1-122001-10000000000
χ293333333333333333-13-13333000000000000-1-1-1-1000000000000-1-1-1-100000000000011-1-1-1-111-1-111-1-1
χ303333333333333333-13-13333000000000000-1-1-1-1000000000000-1-1-1-1000000000000-1-1-1-111-1-111-1-111
χ31333333333-3-333333-1-3-1-3-3-3-3000000000000-1-1-1-100000000000011-1-10000000000001111-1-111-1-1-1-111
χ32333333333-3-333333-1-3-1-3-3-3-3000000000000-1-1-1-100000000000011-1-1000000000000-1-11111-1-11111-1-1
χ3333-333-3-333333-3-3-331-3-133-3-3000000000000-111-1000000000000-11-110000000000001-1-11-111-1-11-11-11
χ3433-333-3-333333-3-3-331-3-133-3-3000000000000-111-1000000000000-11-11000000000000-11-111-1-111-11-11-1
χ3533-333-3-333-3-33-3-3-3313-1-3-333000000000000-111-10000000000001-1-110000000000001-11-1-111-1-111-11-1
χ3633-333-3-333-3-33-3-3-3313-1-3-333000000000000-111-10000000000001-1-11000000000000-111-11-1-111-1-11-11
χ374444-2444-200-2-2-2-2-24040000-2-2-2-2-2-2-2-2-2-2-2-244-2-211111111111100-2-200000000000000000000000000
χ38444-2-2-2-2-2-2001-211140400004-2-244-2-2-2-24-2-2-2-2-2-2-211-211-2-21111001100000000000000000000000000
χ39444-2-2-2-2-2-2001-21114040000-24-2-2-244-2-2-24-2-2-2-2-21-211-2111-2-211001100000000000000000000000000
χ40444-2-2-2-2-2-2001-21114040000-2-24-2-2-2-244-2-24-2-2-2-211-211-21111-2-2001100000000000000000000000000
χ4144-44-2-4-44-200-2222-2-4040000-2-2-2222222-2-2-24-42-2111111-1-1-1-1-1-100-2200000000000000000000000000
χ4244-4-2-222-2-20012-1-11-40400004-2-2-4-422224-2-2-222-2-211-21122-1-1-1-1001-100000000000000000000000000
χ4344-4-2-222-2-20012-1-11-4040000-24-222-4-422-24-2-222-21-211-21-1-122-1-1001-100000000000000000000000000
χ4444-4-2-222-2-20012-1-11-4040000-2-242222-4-4-2-24-222-211-211-2-1-1-1-122001-100000000000000000000000000
χ454-404400-4-44i−4i4000-40004i−4i00111−i3i3−i3i3−i3i3-1-1-10000111-1-1-1−i3i3−i3i3−i3i30000i−ii−ii−i3−33−33−300000000000000
χ464-404400-4-44i−4i4000-40004i−4i00111i3−i3i3−i3i3−i3-1-1-10000111-1-1-1i3−i3i3−i3i3−i30000i−ii−ii−i−33−33−3300000000000000
χ474-404400-4-44i−4i4000-40004i−4i00-2-2-20000002220000-2-2-22220000000000−2i2i−2i2i−2i2i00000000000000000000
χ484-404400-4-4−4i4i4000-4000−4i4i00111−i3i3−i3i3−i3i3-1-1-10000111-1-1-1−i3i3−i3i3−i3i30000−ii−ii−ii−33−33−3300000000000000
χ494-404400-4-4−4i4i4000-4000−4i4i00111i3−i3i3−i3i3−i3-1-1-10000111-1-1-1i3−i3i3−i3i3−i30000−ii−ii−ii3−33−33−300000000000000
χ504-404400-4-4−4i4i4000-4000−4i4i00-2-2-20000002220000-2-2-222200000000002i−2i2i−2i2i−2i00000000000000000000
χ514-40-24−2i32i32-44i−4i-20−2i32i32000−2i2i23−2311-2−i3i3i3−i300-1-12000011-2-1-12−i3i3i3−i3000000i−ii−i−2i2i3−3−330000000000000000
χ524-40-24−2i32i32-44i−4i-20−2i32i32000−2i2i23−231-21i3−i300−i3i3-12-100001-21-12-1i3−i300−i3i30000i−i−2i2ii−i−33003−300000000000000
χ534-40-24−2i32i32-44i−4i-20−2i32i32000−2i2i23−23-21100−i3i3i3−i32-1-10000-2112-1-100−i3i3i3−i30000−2i2ii−ii−i003−3−3300000000000000
χ544-40-24−2i32i32-4−4i4i-20−2i32i320002i−2i−232311-2−i3i3i3−i300-1-12000011-2-1-12−i3i3i3−i3000000−ii−ii2i−2i−333−30000000000000000
χ554-40-24−2i32i32-4−4i4i-20−2i32i320002i−2i−23231-21i3−i300−i3i3-12-100001-21-12-1i3−i300−i3i30000−ii2i−2i−ii3−300−3300000000000000
χ564-40-24−2i32i32-4−4i4i-20−2i32i320002i−2i−2323-21100−i3i3i3−i32-1-10000-2112-1-100−i3i3i3−i300002i−2i−ii−ii00−333−300000000000000
χ574-40-242i3−2i32-44i−4i-202i3−2i32000−2i2i−232311-2i3−i3−i3i300-1-12000011-2-1-12i3−i3−i3i3000000i−ii−i−2i2i−333−30000000000000000
χ584-40-242i3−2i32-44i−4i-202i3−2i32000−2i2i−23231-21−i3i300i3−i3-12-100001-21-12-1−i3i300i3−i30000i−i−2i2ii−i3−300−3300000000000000
χ594-40-242i3−2i32-44i−4i-202i3−2i32000−2i2i−2323-21100i3−i3−i3i32-1-10000-2112-1-100i3−i3−i3i30000−2i2ii−ii−i00−333−300000000000000
χ604-40-242i3−2i32-4−4i4i-202i3−2i320002i−2i23−2311-2i3−i3−i3i300-1-12000011-2-1-12i3−i3−i3i3000000−ii−ii2i−2i3−3−330000000000000000
χ614-40-242i3−2i32-4−4i4i-202i3−2i320002i−2i23−231-21−i3i300i3−i3-12-100001-21-12-1−i3i300i3−i30000−ii2i−2i−ii−33003−300000000000000
χ624-40-242i3−2i32-4−4i4i-202i3−2i320002i−2i23−23-21100i3−i3−i3i32-1-10000-2112-1-100i3−i3−i3i300002i−2i−ii−ii003−3−3300000000000000
χ636666-3666-300-3-3-3-3-3-20-20000000000000000-2-21100000000000000110000000000002200-2-2-1-1110000
χ646666-3666-300-3-3-3-3-3-20-20000000000000000-2-2110000000000000011000000000000-2-2002211-1-10000
χ65666-36-3-3-3666-36-3-3-3-26-2-3-3-3-300000000000011-2-2000000000000-2-21100000000000000110000000000
χ66666-36-3-3-36-6-6-36-3-3-3-2-6-2333300000000000011-2-2000000000000221100000000000000-1-10000000000
χ6766-66-3-6-66-300-3333-320-20000000000000000-22-11000000000000001-10000000000002-200-22-111-10000
χ6866-66-3-6-66-300-3333-320-20000000000000000-22-11000000000000001-1000000000000-22002-21-1-110000
χ6966-6-3633-3666-3-633-32-6-2-3-3330000000000001-12-2000000000000-221-1000000000000001-10000000000
χ7066-6-3633-36-6-6-3-633-326-233-3-30000000000001-12-20000000000002-21-100000000000000-110000000000
χ718-808-400-8400-400040000000222−2i32i3−2i32i3−2i32i3-2-2-20000-1-1-1111i3−i3i3−i3i3−i3000000000000000000000000000000
χ728-808-400-8400-4000400000002222i3−2i32i3−2i32i3−2i3-2-2-20000-1-1-1111−i3i3−i3i3−i3i3000000000000000000000000000000
χ738-808-400-8400-400040000000-4-4-40000004440000222-2-2-2000000000000000000000000000000000000
χ748-80-4-4−4i34i34400202i3−2i3-2000000022-4−2i32i32i3−2i300-2-240000-1-1211-2i3−i3−i3i300000000000000000000000000000000
χ758-80-4-4−4i34i34400202i3−2i3-200000002-422i3−2i300−2i32i3-24-20000-12-11-21−i3i300i3−i3000000000000000000000000000000
χ768-80-4-4−4i34i34400202i3−2i3-20000000-42200−2i32i32i3−2i34-2-200002-1-1-21100i3−i3−i3i3000000000000000000000000000000
χ778-80-4-44i3−4i3440020−2i32i3-2000000022-42i3−2i3−2i32i300-2-240000-1-1211-2−i3i3i3−i300000000000000000000000000000000
χ788-80-4-44i3−4i3440020−2i32i3-200000002-42−2i32i3002i3−2i3-24-20000-12-11-21i3−i300−i3i3000000000000000000000000000000
χ798-80-4-44i3−4i3440020−2i32i3-20000000-422002i3−2i3−2i32i34-2-200002-1-1-21100−i3i3i3−i3000000000000000000000000000000
χ80121212-6-6-6-6-6-6003-6333-40-40000000000000000222200000000000000-1-100000000000000000000000000
χ811212-12-6-666-6-60036-3-3340-400000000000000002-2-2200000000000000-1100000000000000000000000000

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