Finite Group Databasebeta

← Group #11722823

Character table — Group #11722823

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222222222222444444444444666666888812121212121212121212121212121212121212121212121218181818181827272727363636363636
order12443336661212121212123336661212121212122244883612126666666612121212121212122424242424242424248888888861224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111-11-11111111-11-111-1-11-11-111-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111-11-1-1-111111-11-111-1-11-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ51111111111111111111111111111-11-11111111-11-11-1-111-11-11-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ61111111111111111111111111111-11-11-1-11111-11-11-1-111-11-11-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1
χ71111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111
χ911-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1i−i11-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i-11i−ii−iii−i−i-11i−ii−i
χ1011-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1−ii11-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii-11−ii−ii−i−iii-11−ii−ii
χ1111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-11i−i11-1-11-11-111-1-1-11-11-1-111ii−i−iii−i−i1-1i−i−ii−i−iii1-1i−i−ii
χ1211-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-11−ii11-1-11-11-111-1-1-11-11-1-111−i−iii−i−iii1-1−iii−iii−i−i1-1−iii−i
χ1311-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1i−i11-1-1-11-11-1-1111-11-111-1-1ii−i−iii−i−i1-1−iii−i−i−iii1-1−iii−i
χ1411-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1−ii11-1-1-11-11-1-1111-11-111-1-1−i−iii−i−iii1-1i−i−iiii−i−i1-1i−i−ii
χ1511-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111i−i11-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i-11−ii−iiii−i−i-11−ii−ii
χ1611-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111−ii11-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iii-11i−ii−i−i−iii-11i−ii−i
χ17222222-122-1-1-122222-1-12-1-1-1-1-1-122222200-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000002200000000-1-10000
χ18222222-122-1-1-122222-1-12-1-1-1-1-1-1222-22-200-1-1-1-12-2-11-1-1112-2-11-1-11100000000-2-200000000110000
χ19222222-122-1-1-122222-1-12-1-1-1-1-1-122-22-2200-1-1-1-1-221-111-1-1-221-111-1-100000000-2-200000000110000
χ20222222-122-1-1-122222-1-12-1-1-1-1-1-122-2-2-2-200-1-1-1-1-2-2111111-2-2111111000000002200000000-1-10000
χ2122222-122-122222-1-1-12-1-12-122-1-1-1-1020222-1-1-1-10-10200-1-10-10200-1-12-12-1-1-1-1-100002200000000-1-1
χ2222222-122-122222-1-1-12-1-12-122-1-1-1-10202-2-2-1-1-1-10-10200-1-10-10200-1-1-21-2111110000-2-20000000011
χ2322222-122-122222-1-1-12-1-12-122-1-1-1-10-20-222-1-1-1-1010-20011010-200112-12-1-1-1-1-10000-2-20000000011
χ2422222-122-122222-1-1-12-1-12-122-1-1-1-10-20-2-2-2-1-1-1-1010-20011010-20011-21-21111100002200000000-1-1
χ252222-122-12222-1-122-1-12-1-12-1-122-1-1202022-1-1-1-1-1020-1-100-1020-1-100-12-12-1-1-1-1002200000000-1-100
χ262222-122-12222-1-122-1-12-1-12-1-122-1-12020-2-2-1-1-1-1-1020-1-100-1020-1-1001-21-2111100-2-2000000001100
χ272222-122-12222-1-122-1-12-1-12-1-122-1-1-20-2022-1-1-1-110-20110010-201100-12-12-1-1-1-100-2-2000000001100
χ282222-122-12222-1-122-1-12-1-12-1-122-1-1-20-20-2-2-1-1-1-110-20110010-2011001-21-21111002200000000-1-100
χ2922-2-222-122-111-2-2-2-22-1-12-1-11111-2-222-2-200-1-11122-1-1-1-1-1-1-2-211111100000000-22000000001-10000
χ3022-2-222-122-111-2-2-2-22-1-12-1-11111-2-22-2-2200-1-1112-2-11-1-111-221-111-1-1000000002-200000000-110000
χ3122-2-222-122-111-2-2-2-22-1-12-1-11111-2-2-222-200-1-111-221-111-1-12-2-11-1-111000000002-200000000-110000
χ3222-2-222-122-111-2-2-2-22-1-12-1-11111-2-2-2-22200-1-111-2-211111122-1-1-1-1-1-100000000-22000000001-10000
χ3322-2-22-122-12-2-2-2-211-12-1-12-1-2-21111020-22i−2i-1-1110-10200-1-1010-200112i−i−2ii−i−iii00002i−2i00000000−ii
χ3422-2-22-122-12-2-2-2-211-12-1-12-1-2-21111020-2−2i2i-1-1110-10200-1-1010-20011−2ii2i−iii−i−i0000−2i2i00000000i−i
χ3522-2-22-122-12-2-2-2-211-12-1-12-1-2-211110-2022i−2i-1-111010-200110-10200-1-12i−i−2ii−i−iii0000−2i2i00000000i−i
χ3622-2-22-122-12-2-2-2-211-12-1-12-1-2-211110-202−2i2i-1-111010-200110-10200-1-1−2ii2i−iii−i−i00002i−2i00000000−ii
χ3722-2-2-122-122-2-211-2-2-1-12-1-1211-2-21120-202i−2i-1-111-1020-1-10010-201100−i2ii−2i−i−iii002i−2i00000000−ii00
χ3822-2-2-122-122-2-211-2-2-1-12-1-1211-2-21120-20−2i2i-1-111-1020-1-10010-201100i−2i−i2iii−i−i00−2i2i00000000i−i00
χ3922-2-2-122-122-2-211-2-2-1-12-1-1211-2-211-20202i−2i-1-11110-201100-1020-1-100−i2ii−2i−i−iii00−2i2i00000000i−i00
χ4022-2-2-122-122-2-211-2-2-1-12-1-1211-2-211-2020−2i2i-1-11110-201100-1020-1-100i−2i−i2iii−i−i002i−2i00000000−ii00
χ412-22i−2i222-2-2-22i−2i2i−2i2i−2i222-2-2-22i−2i2i−2i2i−2i0000002-22i−2i0000000000000000000000000000002ζ3−2ζ32ζ−2ζ000000
χ422-22i−2i222-2-2-22i−2i2i−2i2i−2i222-2-2-22i−2i2i−2i2i−2i0000002-22i−2i000000000000000000000000000000−2ζ32ζ3−2ζ2ζ000000
χ432-2−2i2i222-2-2-2−2i2i−2i2i−2i2i222-2-2-2−2i2i−2i2i−2i2i0000002-2−2i2i0000000000000000000000000000002ζ−2ζ2ζ3−2ζ3000000
χ442-2−2i2i222-2-2-2−2i2i−2i2i−2i2i222-2-2-2−2i2i−2i2i−2i2i0000002-2−2i2i000000000000000000000000000000−2ζ2ζ−2ζ32ζ3000000
χ4544444-2-24-2-2-2-244-2-2-2-21-2-21-2-211-2-204040011110-20-200110-20-20011000000000000000000000000
χ4644444-2-24-2-2-2-244-2-2-2-21-2-21-2-211-2-20-40-4001111020200-1-1020200-1-1000000000000000000000000
χ474444-24-2-24-2-2-2-2-244-21-2-21-211-2-2-2-24040001111-20-201100-20-201100000000000000000000000000
χ484444-24-2-24-2-2-2-2-244-21-2-21-211-2-2-2-2-40-400011112020-1-1002020-1-100000000000000000000000000
χ494444-2-24-2-2444-2-2-2-21-2-21-2-2-2-2-2-21100004411110000000000000000-2-2-2-211110000000000000000
χ504444-2-24-2-2444-2-2-2-21-2-21-2-2-2-2-2-2110000-4-4111100000000000000002222-1-1-1-10000000000000000
χ5144-4-44-2-24-2-222-4-422-2-21-2-2122-1-122040-40011-1-10-20-20011020200-1-1000000000000000000000000
χ5244-4-44-2-24-2-222-4-422-2-21-2-2122-1-1220-4040011-1-1020200-1-10-20-20011000000000000000000000000
χ5344-4-4-24-2-24-22222-4-4-21-2-21-2-1-1222240-400011-1-1-20-2011002020-1-100000000000000000000000000
χ5444-4-4-24-2-24-22222-4-4-21-2-21-2-1-12222-40400011-1-12020-1-100-20-201100000000000000000000000000
χ5544-4-4-2-24-2-24-4-422221-2-21-2-22222-1-100004i−4i11-1-10000000000000000−2i−2i2i2iii−i−i0000000000000000
χ5644-4-4-2-24-2-24-4-422221-2-21-2-22222-1-10000−4i4i11-1-100000000000000002i2i−2i−2i−i−iii0000000000000000
χ574-44i−4i44-2-4-42−2i2i4i−4i4i−4i4-2-2-422−2i2i−2i2i4i−4i000000-22−2i2i0000000000000000000000000000000000000000
χ584-44i−4i4-24-42-44i−4i4i−4i−2i2i-24-22-424i−4i−2i2i−2i2i000000-22−2i2i0000000000000000000000000000000000000000
χ594-44i−4i4-2-2-422−2i2i4i−4i−2i2i-2-2122-1−2i2ii−i−2i2i0000001-1i−i0000003-30000003i−3i000000000000000000000000
χ604-44i−4i4-2-2-422−2i2i4i−4i−2i2i-2-2122-1−2i2ii−i−2i2i0000001-1i−i000000-33000000−3i3i000000000000000000000000
χ614-44i−4i-2442-4-44i−4i−2i2i4i−4i-2-2422-4−2i2i4i−4i−2i2i000000-22−2i2i0000000000000000000000000000000000000000
χ624-44i−4i-24-22-42−2i2i−2i2i4i−4i-21-22-12i−i−2i2i−2i2i0000001-1i−i00003-30000003i−3i00000000000000000000000000
χ634-44i−4i-24-22-42−2i2i−2i2i4i−4i-21-22-12i−i−2i2i−2i2i0000001-1i−i0000-33000000−3i3i00000000000000000000000000
χ644-44i−4i-2-2422-44i−4i−2i2i−2i2i1-2-2-122−2i2i−2i2ii−i0000001-1i−i000000000000000000003ζ−3ζ3ζ3−3ζ30000000000000000
χ654-44i−4i-2-2422-44i−4i−2i2i−2i2i1-2-2-122−2i2i−2i2ii−i0000001-1i−i00000000000000000000−3ζ3ζ−3ζ33ζ30000000000000000
χ664-4−4i4i44-2-4-422i−2i−4i4i−4i4i4-2-2-4222i−2i2i−2i−4i4i000000-222i−2i0000000000000000000000000000000000000000
χ674-4−4i4i4-24-42-4−4i4i−4i4i2i−2i-24-22-42−4i4i2i−2i2i−2i000000-222i−2i0000000000000000000000000000000000000000
χ684-4−4i4i4-2-2-4222i−2i−4i4i2i−2i-2-2122-12i−2i−ii2i−2i0000001-1−ii0000003-3000000−3i3i000000000000000000000000
χ694-4−4i4i4-2-2-4222i−2i−4i4i2i−2i-2-2122-12i−2i−ii2i−2i0000001-1−ii000000-330000003i−3i000000000000000000000000
χ704-4−4i4i-2442-4-4−4i4i2i−2i−4i4i-2-2422-42i−2i−4i4i2i−2i000000-222i−2i0000000000000000000000000000000000000000
χ714-4−4i4i-24-22-422i−2i2i−2i−4i4i-21-22-12−ii2i−2i2i−2i0000001-1−ii00003-3000000−3i3i00000000000000000000000000
χ724-4−4i4i-24-22-422i−2i2i−2i−4i4i-21-22-12−ii2i−2i2i−2i0000001-1−ii0000-330000003i−3i00000000000000000000000000
χ734-4−4i4i-2-2422-4−4i4i2i−2i2i−2i1-2-2-1222i−2i2i−2i−ii0000001-1−ii000000000000000000003ζ3−3ζ33ζ−3ζ0000000000000000
χ744-4−4i4i-2-2422-4−4i4i2i−2i2i−2i1-2-2-1222i−2i2i−2i−ii0000001-1−ii00000000000000000000−3ζ33ζ3−3ζ3ζ0000000000000000
χ758888-4-4-4-4-4-4-4-4-4-4-4-4222222222222000000-1-1-1-10000000000000000000000000000000000000000
χ7688-8-8-4-4-4-4-4-4444444222222-2-2-2-2-2-2000000-1-1110000000000000000000000000000000000000000
χ778-88i−8i-4-4-4444−4i4i−4i4i−4i4i222-2-2-22i−2i2i−2i2i−2i000000-11−ii0000000000000000000000000000000000000000
χ788-8−8i8i-4-4-44444i−4i4i−4i4i−4i222-2-2-2−2i2i−2i2i−2i2i000000-11i−i0000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.