Finite Group Databasebeta

← Group #13167564

Character table — Group #13167564

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222224444444444888888888888888888889918181818181818363636363636363636363636363636363636363636367272727272727272
order12222366633666666663366666666666666666622222666622444444444466121212121212121266121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ5111-1-1111111-1-11-1-1-1-11111-11-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-11-1ii−i−iii−i−i11iiii−i−i−i−i1-11-1ii−i−i
χ6111-1-1111111-1-11-1-1-1-11111-11-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-11-1−i−iii−i−iii11−i−i−i−iiiii1-11-1−i−iii
χ7111-1-1111111-1-11-1-1-1-11111-11-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11ii−i−i−i−iii11−i−i−i−iiiii-11-11ii−i−i
χ8111-1-1111111-1-11-1-1-1-11111-11-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11−i−iiiii−i−i11iiii−i−i−i−i-11-11−i−iii
χ911-11-111-1-1111-1111-1-1111-11-1-111-1-1-1-11111-1-1-1-1111-1-111-1-111-1-1i−ii−ii−ii−i1-1ii−i−iii−i−i11-1-1i−ii−i
χ1011-11-111-1-1111-1111-1-1111-11-1-111-1-1-1-11111-1-1-1-1111-1-111-1-111-1-1−ii−ii−ii−ii1-1−i−iii−i−iii11-1-1−ii−ii
χ1111-11-111-1-1111-1111-1-1111-11-1-111-1-1-1-11111-1-1-1-1111-1-111-1-1-1-111i−ii−i−ii−ii1-1−i−iii−i−iii-1-111i−ii−i
χ1211-11-111-1-1111-1111-1-1111-11-1-111-1-1-1-11111-1-1-1-1111-1-111-1-1-1-111−ii−iii−ii−i1-1ii−i−iii−i−i-1-111−ii−ii
χ1311-1-1111-1-111-111-1-111111-1-1-1111-1-1-1-1-1-1-1-11111-1-11-11-1-1111-1-111-1-111-1-111-111-1-1-1-1111-1-111-1-11
χ1411-1-1111-1-111-111-1-111111-1-1-1111-1-1-1-1-1-1-1-11111-1-11-11-1-1111-1-11-111-1-111-11-1-1-11111-1-11-1-11-111-1
χ1511-1-1111-1-111-111-1-111111-1-1-1111-1-1-1-1-1-1-1-11111-1-11-11-1-111-111-11-1-11-111-11-1-1-11111-1-1-111-11-1-11
χ1611-1-1111-1-111-111-1-111111-1-1-1111-1-1-1-1-1-1-1-11111-1-11-11-1-111-111-1-111-11-1-111-111-1-1-1-111-111-1-111-1
χ17222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2000000000000-2-20000000000000000
χ1822222-1-1-1-122-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-100000000
χ1922222-1-1-1-122-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-100000000-2-2-2-2-1-11111111100000000
χ2022222-1-1-1-122-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-21111000000000000113−33−33−33−300000000
χ2122222-1-1-1-122-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2111100000000000011−33−33−33−3300000000
χ22222-2-2222222-2-22-2-2-2-22222-22-2222222-2-2-2-2-2-2-2-222-2-222222000000000000-2-20000000000000000
χ23222-2-2-1-1-1-122112-2-2-2-22-1-12-22-2-1-1-1-1-1-11111111122-2-22-1-1-1-100000000000011−i3i3−i3i3i3−i3i3−i300000000
χ24222-2-2-1-1-1-122112-2-2-2-22-1-12-22-2-1-1-1-1-1-11111111122-2-22-1-1-1-100000000000011i3−i3i3−i3−i3i3−i3i300000000
χ25222-2-2-1-1-1-122112-2-2-2-22-1-12-22-2-1-1-1-1-1-111111111-2-222-21111000000002i2i−2i−2i-1-1−i−i−i−iiiii00000000
χ26222-2-2-1-1-1-122112-2-2-2-22-1-12-22-2-1-1-1-1-1-111111111-2-222-2111100000000−2i−2i2i2i-1-1iiii−i−i−i−i00000000
χ2722-22-222-2-2222-2222-2-2222-22-2-222-2-2-2-22222-2-2-2-2-2-2-222-2-222000000000000-220000000000000000
χ2822-22-2-1-11122-11222-2-22-1-1-22-2-2-1-11111-1-1-1-11111222-2-2-1-111000000002i−2i2i−2i-11−i−iii−i−iii00000000
χ2922-22-2-1-11122-11222-2-22-1-1-22-2-2-1-11111-1-1-1-11111222-2-2-1-11100000000−2i2i−2i2i-11ii−i−iii−i−i00000000
χ3022-22-2-1-11122-11222-2-22-1-1-22-2-2-1-11111-1-1-1-11111-2-2-22211-1-10000000000001-1−i3i3i3−i3−i3i3i3−i300000000
χ3122-22-2-1-11122-11222-2-22-1-1-22-2-2-1-11111-1-1-1-11111-2-2-22211-1-10000000000001-1i3−i3−i3i3i3−i3−i3i300000000
χ3222-2-2222-2-222-222-2-222222-2-2-2222-2-2-2-2-2-2-2-2222222-22-222-2-2000000000000-220000000000000000
χ3322-2-22-1-111221-12-2-2222-1-1-2-2-22-1-111111111-1-1-1-122-22-2-1-1110000000000001-13−3−33−333−300000000
χ3422-2-22-1-111221-12-2-2222-1-1-2-2-22-1-111111111-1-1-1-122-22-2-1-1110000000000001-1−333−33−3−3300000000
χ3522-2-22-1-111221-12-2-2222-1-1-2-2-22-1-111111111-1-1-1-1-2-22-2211-1-1000000002-2-22-11-1-11111-1-100000000
χ3622-2-22-1-111221-12-2-2222-1-1-2-2-22-1-111111111-1-1-1-1-2-22-2211-1-100000000-222-2-1111-1-1-1-11100000000
χ374444444441-2441-2-211-21-211-2-21-211-2-211-2-211-2-200000000000002222000000000000000000-1-1-1-1
χ384444444441-2441-2-211-21-211-2-21-211-2-211-2-211-2-20000000000000-2-2-2-20000000000000000001111
χ39444444444-2144-211-2-21-21-2-211-21-2-211-2-211-2-2110000000002222000000000000000000-1-1-1-10000
χ40444444444-2144-211-2-21-21-2-211-21-2-211-2-211-2-211000000000-2-2-2-200000000000000000011110000
χ41444-4-444441-2-4-4122-1-1-21-21-1-221-211-2-2-1-122-1-12200000000000002i2i−2i−2i000000000000000000−i−iii
χ42444-4-444441-2-4-4122-1-1-21-21-1-221-211-2-2-1-122-1-1220000000000000−2i−2i2i2i000000000000000000ii−i−i
χ43444-4-44444-21-4-4-2-1-1221-21-221-1-21-2-21122-1-122-1-10000000002-22-2000000000000000000-11-110000
χ44444-4-44444-21-4-4-2-1-1221-21-221-1-21-2-21122-1-122-1-1000000000-22-220000000000000000001-11-10000
χ4544-44-444-4-41-24-41-2-2-1-1-21-2-11221-2-1-12211-2-2-1-12200000000000002i−2i2i−2i000000000000000000−ii−ii
χ4644-44-444-4-41-24-41-2-2-1-1-21-2-11221-2-1-12211-2-2-1-1220000000000000−2i2i−2i2i000000000000000000i−ii−i
χ4744-44-444-4-4-214-4-211221-212-2-1-1-2122-1-1-2-21122-1-100000000022-2-2000000000000000000-1-1110000
χ4844-44-444-4-4-214-4-211221-212-2-1-1-2122-1-1-2-21122-1-1000000000-2-22200000000000000000011-1-10000
χ4944-4-4444-4-41-2-4412211-21-2-1-12-21-2-1-122-1-12211-2-200000000000002-2-22000000000000000000-111-1
χ5044-4-4444-4-41-2-4412211-21-2-1-12-21-2-1-122-1-12211-2-20000000000000-222-20000000000000000001-1-11
χ5144-4-4444-4-4-21-44-2-1-1-2-21-2122-11-2122-1-122-1-1-2-2110000000002-2-22000000000000000000-111-10000
χ5244-4-4444-4-4-21-44-2-1-1-2-21-2122-11-2122-1-122-1-1-2-211000000000-222-20000000000000000001-1-110000
χ534-40004-4004400-40000-4440000-4-40000000000004-40004-400000000000000000000000000000000
χ544-40004-4004400-40000-4440000-4-4000000000000-44000-4400000000000000000000000000000000
χ554-4000-22−2i32i34400-40000-4-2-2000022−2i32i3−2i32i3000000004-4000-22−2i32i3000000000000000000000000000000
χ564-4000-22−2i32i34400-40000-4-2-2000022−2i32i3−2i32i300000000-440002-22i3−2i3000000000000000000000000000000
χ574-4000-222i3−2i34400-40000-4-2-20000222i3−2i32i3−2i3000000004-4000-222i3−2i3000000000000000000000000000000
χ584-4000-222i3−2i34400-40000-4-2-20000222i3−2i32i3−2i300000000-440002-2−2i32i3000000000000000000000000000000
χ5988888-4-4-4-42-4-4-42-4-422-4-1222-4-4-12-1-122-1-122-1-122000000000000000000000000000000000000000
χ6088888-4-4-4-4-42-4-4-422-4-422-1-4-4222-122-1-122-1-122-1-1000000000000000000000000000000000000000
χ61888-8-8-4-4-4-42-444244-2-2-4-122-2-44-12-1-12211-2-211-2-2000000000000000000000000000000000000000
χ62888-8-8-4-4-4-4-4244-4-2-24422-1-442-22-122-1-1-2-211-2-211000000000000000000000000000000000000000
χ6388-88-8-4-4442-4-442-4-4-2-2-4-12-2244-1211-2-2-1-12211-2-2000000000000000000000000000000000000000
χ6488-88-8-4-444-42-44-4224422-14-4-2-22-1-2-21122-1-1-2-211000000000000000000000000000000000000000
χ6588-8-88-4-4442-44-424422-4-12-2-24-4-1211-2-211-2-2-1-122000000000000000000000000000000000000000
χ6688-8-88-4-444-424-4-4-2-2-4-422-144-222-1-2-211-2-21122-1-1000000000000000000000000000000000000000
χ678-80008-8002-400-2006-642-40000-24000000006-600000000000000000000000000000000000000000
χ688-80008-8002-400-200-6642-40000-2400000000-6600000000000000000000000000000000000000000
χ698-80008-800-420046-600-2-4200004-20000006-60000000000000000000000000000000000000000000
χ708-80008-800-42004-6600-2-4200004-2000000-660000000000000000000000000000000000000000000
χ718-8000-44−4i34i32-400-2006-64-1200001-2−i3i32i3−2i3−3i33i300-3300000000000000000000000000000000000000000
χ728-8000-44−4i34i32-400-200-664-1200001-2−i3i32i3−2i33i3−3i3003-300000000000000000000000000000000000000000
χ738-8000-44−4i34i3-420046-600-22-10000-212i3−2i3−i3i300-3300−3i33i3000000000000000000000000000000000000000
χ748-8000-44−4i34i3-42004-6600-22-10000-212i3−2i3−i3i3003-3003i3−3i3000000000000000000000000000000000000000
χ758-8000-444i3−4i32-400-2006-64-1200001-2i3−i3−2i32i33i3−3i300-3300000000000000000000000000000000000000000
χ768-8000-444i3−4i32-400-200-664-1200001-2i3−i3−2i32i3−3i33i3003-300000000000000000000000000000000000000000
χ778-8000-444i3−4i3-420046-600-22-10000-21−2i32i3i3−i300-33003i3−3i3000000000000000000000000000000000000000
χ788-8000-444i3−4i3-42004-6600-22-10000-21−2i32i3i3−i3003-300−3i33i3000000000000000000000000000000000000000

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