Finite Group Databasebeta

← Group #72341308

Character table — Group #72341308

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11114444661212121212121212121212122424242424243232323232323232484848481111444466121212121212121212121212242424242424323232323232323248484848
order1222444422224444444444224444366612121212448822224444222244444444442244446666121212124488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111-1-1-1-1-1-1-1-11-1-111-1-111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11-1-111-1-111111111-1-1-1-1
χ31111-1-1-1-1111111111-1-1-1-11-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1111111111-1-1-1-11-1-1-1-1111111-1-1-1-111-1-1
χ41111-1-1-1-111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-111
χ51-11-1ii−i−i1-11-1-1ii−i−i11-1-111-1i−ii−i11-1-1ii−i−ii−i1-11-11-1ii−i−i1-11-1-1ii−i−i11-1-111-1i−ii−i11-1-1ii−i−ii−i1-1
χ61-11-1ii−i−i1-11-1-1−i−iii-1-1111-11i−i−ii11-1-1ii−i−i−ii-111-11-1ii−i−i1-11-1-1−i−iii-1-1111-11i−i−ii11-1-1ii−i−i−ii-11
χ71-11-1−i−iii1-11-1-1ii−i−i-1-1111-11−iii−i11-1-1−i−iiii−i-111-11-1−i−iii1-11-1-1ii−i−i-1-1111-11−iii−i11-1-1−i−iiii−i-11
χ81-11-1−i−iii1-11-1-1−i−iii11-1-111-1−ii−ii11-1-1−i−iii−ii1-11-11-1−i−iii1-11-1-1−i−iii11-1-111-1−ii−ii11-1-1−i−iii−ii1-1
χ92222222222222000000002002200-1-1-1-1-1-1-1-100002222222222222000000002002200-1-1-1-1-1-1-1-10000
χ102222-2-2-2-22222200000000200-2-200-1-1-1-1111100002222-2-2-2-22222200000000200-2-200-1-1-1-111110000
χ112-22-22i2i−2i−2i2-22-2-2000000002002i−2i00-1-111−i−iii00002-22-22i2i−2i−2i2-22-2-2000000002002i−2i00-1-111−i−iii0000
χ122-22-2−2i−2i2i2i2-22-2-200000000200−2i2i00-1-111ii−i−i00002-22-2−2i−2i2i2i2-22-2-200000000200−2i2i00-1-111ii−i−i0000
χ133333333333-1-1-111111111-111-1-11100000000-1-1-1-13333333333-1-1-111111111-111-1-11100000000-1-1-1-1
χ143333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000011113333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000001111
χ153333-3-3-3-333-1-1-11111-1-1-1-1-1-1-1111100000000-1-1113333-3-3-3-333-1-1-11111-1-1-1-1-1-1-1111100000000-1-111
χ163333-3-3-3-333-1-1-1-1-1-1-11111-11111-1-10000000011-1-13333-3-3-3-333-1-1-1-1-1-1-11111-11111-1-10000000011-1-1
χ173-33-33i3i−3i−3i3-3-111ii−i−i11-1-1-11-1−iii−i00000000−ii-113-33-33i3i−3i−3i3-3-111ii−i−i11-1-1-11-1−iii−i00000000−ii-11
χ183-33-33i3i−3i−3i3-3-111−i−iii-1-111-1-11−ii−ii00000000i−i1-13-33-33i3i−3i−3i3-3-111−i−iii-1-111-1-11−ii−ii00000000i−i1-1
χ193-33-3−3i−3i3i3i3-3-111ii−i−i-1-111-1-11i−ii−i00000000−ii1-13-33-3−3i−3i3i3i3-3-111ii−i−i-1-111-1-11i−ii−i00000000−ii1-1
χ203-33-3−3i−3i3i3i3-3-111−i−iii11-1-1-11-1i−i−ii00000000i−i-113-33-3−3i−3i3i3i3-3-111−i−iii11-1-1-11-1i−i−ii00000000i−i-11
χ2144-4-42i−2i2i−2i000002i−2i2i−2i2-22-200000001-11-1i−ii−i000044-4-42i−2i2i−2i000002i−2i2i−2i2-22-200000001-11-1i−ii−i0000
χ2244-4-42i−2i2i−2i00000−2i2i−2i2i-22-2200000001-11-1i−ii−i000044-4-42i−2i2i−2i00000−2i2i−2i2i-22-2200000001-11-1i−ii−i0000
χ2344-4-4−2i2i−2i2i000002i−2i2i−2i-22-2200000001-11-1−ii−ii000044-4-4−2i2i−2i2i000002i−2i2i−2i-22-2200000001-11-1−ii−ii0000
χ2444-4-4−2i2i−2i2i00000−2i2i−2i2i2-22-200000001-11-1−ii−ii000044-4-4−2i2i−2i2i00000−2i2i−2i2i2-22-200000001-11-1−ii−ii0000
χ254-4-442-2-22000002-2-222-2-2200000001-1-111-1-1100004-4-442-2-22000002-2-222-2-2200000001-1-111-1-110000
χ264-4-442-2-2200000-222-2-222-200000001-1-111-1-1100004-4-442-2-2200000-222-2-222-200000001-1-111-1-110000
χ274-4-44-222-2000002-2-22-222-200000001-1-11-111-100004-4-44-222-2000002-2-22-222-200000001-1-11-111-10000
χ284-4-44-222-200000-222-22-2-2200000001-1-11-111-100004-4-44-222-200000-222-22-2-2200000001-1-11-111-10000
χ2966660000-2-222-222220000-20000-2-200000000000066660000-2-222-222220000-20000-2-2000000000000
χ3066660000-2-222-2-2-2-2-20000-200002200000000000066660000-2-222-2-2-2-2-20000-2000022000000000000
χ3166660000-2-2-2-22000022222-2-2000000000000000066660000-2-2-2-22000022222-2-20000000000000000
χ3266660000-2-2-2-220000-2-2-2-2222000000000000000066660000-2-2-2-220000-2-2-2-22220000000000000000
χ336-66-60000-222-222i2i−2i−2i0000-20000−2i2i0000000000006-66-60000-222-222i2i−2i−2i0000-20000−2i2i000000000000
χ346-66-60000-222-22−2i−2i2i2i0000-200002i−2i0000000000006-66-60000-222-22−2i−2i2i2i0000-200002i−2i000000000000
χ356-66-60000-22-22-2000022-2-22-2200000000000000006-66-60000-22-22-2000022-2-22-220000000000000000
χ366-66-60000-22-22-20000-2-22222-200000000000000006-66-60000-22-22-20000-2-22222-20000000000000000
χ3788-8-84i−4i4i−4i00000000000000000000-11-11−ii−ii000088-8-84i−4i4i−4i00000000000000000000-11-11−ii−ii0000
χ3888-8-8−4i4i−4i4i00000000000000000000-11-11i−ii−i000088-8-8−4i4i−4i4i00000000000000000000-11-11i−ii−i0000
χ398-8-884-4-4400000000000000000000-111-1-111-100008-8-884-4-4400000000000000000000-111-1-111-10000
χ408-8-88-444-400000000000000000000-111-11-1-1100008-8-88-444-400000000000000000000-111-11-1-110000
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ421111111111111-1-1-1-1-1-1-1-11-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-111-1-1-1-1-1-1-1-11111
χ431111-1-1-1-1111111111-1-1-1-11-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-11111-1-111
χ441111-1-1-1-111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ451-11-1ii−i−i1-11-1-1ii−i−i11-1-111-1i−ii−i11-1-1ii−i−ii−i1-1-11-11−i−iii-11-111−i−iii-1-111-1-11−ii−ii-1-111−i−iii−ii-11
χ461-11-1ii−i−i1-11-1-1−i−iii-1-1111-11i−i−ii11-1-1ii−i−i−ii-11-11-11−i−iii-11-111ii−i−i11-1-1-11-1−iii−i-1-111−i−iiii−i1-1
χ471-11-1−i−iii1-11-1-1ii−i−i-1-1111-11−iii−i11-1-1−i−iiii−i-11-11-11ii−i−i-11-111−i−iii11-1-1-11-1i−i−ii-1-111ii−i−i−ii1-1
χ481-11-1−i−iii1-11-1-1−i−iii11-1-111-1−ii−ii11-1-1−i−iii−ii1-1-11-11ii−i−i-11-111ii−i−i-1-111-1-11i−ii−i-1-111ii−i−ii−i-11
χ492222222222222000000002002200-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-2-2-2-2-200000000-200-2-200111111110000
χ502222-2-2-2-22222200000000200-2-200-1-1-1-111110000-2-2-2-22222-2-2-2-2-200000000-20022001111-1-1-1-10000
χ512-22-22i2i−2i−2i2-22-2-2000000002002i−2i00-1-111−i−iii0000-22-22−2i−2i2i2i-22-22200000000-200−2i2i0011-1-1ii−i−i0000
χ522-22-2−2i−2i2i2i2-22-2-200000000200−2i2i00-1-111ii−i−i0000-22-222i2i−2i−2i-22-22200000000-2002i−2i0011-1-1−i−iii0000
χ533333333333-1-1-111111111-111-1-11100000000-1-1-1-1-3-3-3-3-3-3-3-3-3-3111-1-1-1-1-1-1-1-11-1-111-1-1000000001111
χ543333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000001111-3-3-3-3-3-3-3-3-3-311111111111111111100000000-1-1-1-1
χ553333-3-3-3-333-1-1-11111-1-1-1-1-1-1-1111100000000-1-111-3-3-3-33333-3-3111-1-1-1-11111111-1-1-1-10000000011-1-1
χ563333-3-3-3-333-1-1-1-1-1-1-11111-11111-1-10000000011-1-1-3-3-3-33333-3-31111111-1-1-1-11-1-1-1-11100000000-1-111
χ573-33-33i3i−3i−3i3-3-111ii−i−i11-1-1-11-1−iii−i00000000−ii-11-33-33−3i−3i3i3i-331-1-1−i−iii-1-1111-11i−i−ii00000000i−i1-1
χ583-33-33i3i−3i−3i3-3-111−i−iii-1-111-1-11−ii−ii00000000i−i1-1-33-33−3i−3i3i3i-331-1-1ii−i−i11-1-111-1i−ii−i00000000−ii-11
χ593-33-3−3i−3i3i3i3-3-111ii−i−i-1-111-1-11i−ii−i00000000−ii1-1-33-333i3i−3i−3i-331-1-1−i−iii11-1-111-1−ii−ii00000000i−i-11
χ603-33-3−3i−3i3i3i3-3-111−i−iii11-1-1-11-1i−i−ii00000000i−i-11-33-333i3i−3i−3i-331-1-1ii−i−i-1-1111-11−iii−i00000000−ii1-1
χ6144-4-42i−2i2i−2i000002i−2i2i−2i2-22-200000001-11-1i−ii−i0000-4-444−2i2i−2i2i00000−2i2i−2i2i-22-220000000-11-11−ii−ii0000
χ6244-4-42i−2i2i−2i00000−2i2i−2i2i-22-2200000001-11-1i−ii−i0000-4-444−2i2i−2i2i000002i−2i2i−2i2-22-20000000-11-11−ii−ii0000
χ6344-4-4−2i2i−2i2i000002i−2i2i−2i-22-2200000001-11-1−ii−ii0000-4-4442i−2i2i−2i00000−2i2i−2i2i2-22-20000000-11-11i−ii−i0000
χ6444-4-4−2i2i−2i2i00000−2i2i−2i2i2-22-200000001-11-1−ii−ii0000-4-4442i−2i2i−2i000002i−2i2i−2i-22-220000000-11-11i−ii−i0000
χ654-4-442-2-22000002-2-222-2-2200000001-1-111-1-110000-444-4-222-200000-222-2-222-20000000-111-1-111-10000
χ664-4-442-2-2200000-222-2-222-200000001-1-111-1-110000-444-4-222-2000002-2-222-2-220000000-111-1-111-10000
χ674-4-44-222-2000002-2-22-222-200000001-1-11-111-10000-444-42-2-2200000-222-22-2-220000000-111-11-1-110000
χ684-4-44-222-200000-222-22-2-2200000001-1-11-111-10000-444-42-2-22000002-2-22-222-20000000-111-11-1-110000
χ6966660000-2-222-222220000-20000-2-2000000000000-6-6-6-6000022-2-22-2-2-2-200002000022000000000000
χ7066660000-2-222-2-2-2-2-20000-2000022000000000000-6-6-6-6000022-2-222222000020000-2-2000000000000
χ7166660000-2-2-2-22000022222-2-20000000000000000-6-6-6-600002222-20000-2-2-2-2-2220000000000000000
χ7266660000-2-2-2-220000-2-2-2-22220000000000000000-6-6-6-600002222-200002222-2-2-20000000000000000
χ736-66-60000-222-222i2i−2i−2i0000-20000−2i2i000000000000-66-6600002-2-22-2−2i−2i2i2i0000200002i−2i000000000000
χ746-66-60000-222-22−2i−2i2i2i0000-200002i−2i000000000000-66-6600002-2-22-22i2i−2i−2i000020000−2i2i000000000000
χ756-66-60000-22-22-2000022-2-22-220000000000000000-66-6600002-22-220000-2-222-22-20000000000000000
χ766-66-60000-22-22-20000-2-22222-20000000000000000-66-6600002-22-22000022-2-2-2-220000000000000000
χ7788-8-84i−4i4i−4i00000000000000000000-11-11−ii−ii0000-8-888−4i4i−4i4i000000000000000000001-11-1i−ii−i0000
χ7888-8-8−4i4i−4i4i00000000000000000000-11-11i−ii−i0000-8-8884i−4i4i−4i000000000000000000001-11-1−ii−ii0000
χ798-8-884-4-4400000000000000000000-111-1-111-10000-888-8-444-4000000000000000000001-1-111-1-110000
χ808-8-88-444-400000000000000000000-111-11-1-110000-888-84-4-44000000000000000000001-1-11-111-10000

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