Finite Group Databasebeta

← Group #11722827

Character table — Group #11722827

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222222222222444444444444666666888812121212121212121212121212121212121212121212121218181818181827272727363636363636
order12443336661212121212123336661212121212128888883612122424242424242424242424242424242424242424242424242224448888666121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1111111111111-1-1-1-111111111-1-1-1-11-1-11-1-1-1-1-1-11-1-11-1-1
χ3111111111111111111111111111111-1-11111111111-1-1-1-111111111-1-1-1-11111-11-1-11-1-1-1-1-1-11-1-11-1
χ4111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-111111-1-11-1-11
χ51111111111111111111111111111-1-111111111-1-1-1-111111111-1-1-1-111111111-1-11-1-11-1-1-1-1-1-11-1-11
χ61111111111111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-11-11111-11-1-11-1
χ71111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11-1-111111-1-11-1-1
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
χ911-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−ii−ii−i11-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i11-1-1-11ii−i−i11-1-1-11
χ1011-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−ii−i−ii11-1-1ii−i−iii−i−i−i−iiiii−i−iii−i−i−i−iii1-11-11-1−i−iii1-11-11-1
χ1111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−i−iii−i11-1-1ii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i-1111-1-1−i−iii-1111-1-1
χ1211-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−i−ii−ii11-1-1ii−i−i−i−iii−i−iiiii−i−i−i−iii−i−iii-1-1-1111ii−i−i-1-1-1111
χ1311-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−iii−ii−i11-1-1−i−iiiii−i−iii−i−i−i−iiiii−i−iii−i−i-1-1-1111−i−iii-1-1-1111
χ1411-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−iii−i−ii11-1-1−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iii-1111-1-1ii−i−i-1111-1-1
χ1511-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−ii−iii−i11-1-1−i−iii−i−iiiii−i−i−i−iii−i−iiiii−i−i1-11-11-1ii−i−i1-11-11-1
χ1611-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−ii−ii−ii11-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii11-1-1-11−i−iii11-1-1-11
χ17222222-122-12222-1-12-1-12-1-122-1-1-1-1002222-1-1-1-100002-12-12-12-10000-1-1-1-1-1-1-1-1002002000000-100-1
χ18222222-122-12222-1-12-1-12-1-122-1-1-1-10022-2-2-1-1-1-100002-12-1-21-210000-1-1-1-1111100-200-20000001001
χ19222222-122-12222-1-12-1-12-1-122-1-1-1-100-2-222-1-1-1-10000-21-212-12-100001111-1-1-1-100-200-20000001001
χ20222222-122-12222-1-12-1-12-1-122-1-1-1-100-2-2-2-2-1-1-1-10000-21-21-21-21000011111111002002000000-100-1
χ2122222-122-1222-1-122-12-1-12-1-1-122-1-1220022-1-1-1-12-12-10000-12-12-1-1-1-10000-1-1-1-102002000000-100-10
χ2222222-122-1222-1-122-12-1-12-1-1-122-1-12200-2-2-1-1-1-12-12-100001-21-2-1-1-1-1000011110-200-200000010010
χ2322222-122-1222-1-122-12-1-12-1-1-122-1-1-2-20022-1-1-1-1-21-210000-12-1211110000-1-1-1-10-200-200000010010
χ2422222-122-1222-1-122-12-1-12-1-1-122-1-1-2-200-2-2-1-1-1-1-21-2100001-21-211110000111102002000000-100-10
χ252222-122-122-1-12222-1-12-1-12-1-1-1-122222200-1-1-1-1-12-12-12-120000-1-1-1-1-1-1-1-100002002000000-100-100
χ262222-122-122-1-12222-1-12-1-12-1-1-1-12222-2-200-1-1-1-1-12-121-21-20000-1-1-1-111110000-200-2000000100100
χ272222-122-122-1-12222-1-12-1-12-1-1-1-122-2-22200-1-1-1-11-21-2-12-1200001111-1-1-1-10000-200-2000000100100
χ282222-122-122-1-12222-1-12-1-12-1-1-1-122-2-2-2-200-1-1-1-11-21-21-21-200001111111100002002000000-100-100
χ2922-2-222-122-1-2-2-2-2112-1-12-1-1-2-21111002i−2i2i−2i-1-11100002i−i−2ii2i−i−2ii0000−i−iii−i−iii00-2002000000100-1
χ3022-2-222-122-1-2-2-2-2112-1-12-1-1-2-21111002i−2i−2i2i-1-11100002i−i−2ii−2ii2i−i0000−i−iiiii−i−i00200-2000000-1001
χ3122-2-222-122-1-2-2-2-2112-1-12-1-1-2-2111100−2i2i2i−2i-1-1110000−2ii2i−i2i−i−2ii0000ii−i−i−i−iii00200-2000000-1001
χ3222-2-222-122-1-2-2-2-2112-1-12-1-1-2-2111100−2i2i−2i2i-1-1110000−2ii2i−i−2ii2i−i0000ii−i−iii−i−i00-2002000000100-1
χ3322-2-22-122-12-2-211-2-2-12-1-12-111-2-2112i−2i002i−2i-1-1112i−i−2ii0000−i2ii−2i−i−iii0000−i−iii0200-2000000-10010
χ3422-2-22-122-12-2-211-2-2-12-1-12-111-2-2112i−2i00−2i2i-1-1112i−i−2ii0000i−2i−i2i−i−iii0000ii−i−i0-2002000000100-10
χ3522-2-22-122-12-2-211-2-2-12-1-12-111-2-211−2i2i002i−2i-1-111−2ii2i−i0000−i2ii−2iii−i−i0000−i−iii0-2002000000100-10
χ3622-2-22-122-12-2-211-2-2-12-1-12-111-2-211−2i2i00−2i2i-1-111−2ii2i−i0000i−2i−i2iii−i−i0000ii−i−i0200-2000000-10010
χ3722-2-2-122-12211-2-2-2-2-1-12-1-121111-2-22i−2i2i−2i00-1-111−i2ii−2i−i2ii−2i0000−i−iii−i−iii0000200-2000000-100100
χ3822-2-2-122-12211-2-2-2-2-1-12-1-121111-2-22i−2i−2i2i00-1-111−i2ii−2ii−2i−i2i0000−i−iiiii−i−i0000-2002000000100-100
χ3922-2-2-122-12211-2-2-2-2-1-12-1-121111-2-2−2i2i2i−2i00-1-111i−2i−i2i−i2ii−2i0000ii−i−i−i−iii0000-2002000000100-100
χ4022-2-2-122-12211-2-2-2-2-1-12-1-121111-2-2−2i2i−2i2i00-1-111i−2i−i2ii−2i−i2i0000ii−i−iii−i−i0000200-2000000-100100
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
χ4544444-2-24-2-244-2-2-2-2-2-21-2-21-2-2-2-211000044111100000000-2-2-2-20000000011110000000000000000
χ4644444-2-24-2-244-2-2-2-2-2-21-2-21-2-2-2-2110000-4-4111100000000222200000000-1-1-1-10000000000000000
χ474444-24-2-24-2-2-244-2-2-21-2-21-2-2-211-2-200440011110000-2-2-2-200000000111100000000000000000000
χ484444-24-2-24-2-2-244-2-2-21-2-21-2-2-211-2-200-4-40011110000222200000000-1-1-1-100000000000000000000
χ494444-2-24-2-24-2-2-2-2441-2-21-2-211-2-2-2-24400001111-2-2-2-2000000001111000000000000000000000000
χ504444-2-24-2-24-2-2-2-2441-2-21-2-211-2-2-2-2-4-400001111222200000000-1-1-1-1000000000000000000000000
χ5144-4-44-2-24-2-2-4-42222-2-21-2-212222-1-100004i−4i11-1-100000000−2i−2i2i2i00000000ii−i−i0000000000000000
χ5244-4-44-2-24-2-2-4-42222-2-21-2-212222-1-10000−4i4i11-1-1000000002i2i−2i−2i00000000−i−iii0000000000000000
χ5344-4-4-24-2-24-222-4-422-21-2-21-222-1-122004i−4i0011-1-10000−2i−2i2i2i00000000ii−i−i00000000000000000000
χ5444-4-4-24-2-24-222-4-422-21-2-21-222-1-12200−4i4i0011-1-100002i2i−2i−2i00000000−i−iii00000000000000000000
χ5544-4-4-2-24-2-242222-4-41-2-21-2-2-1-122224i−4i000011-1-1−2i−2i2i2i00000000ii−i−i000000000000000000000000
χ5644-4-4-2-24-2-242222-4-41-2-21-2-2-1-12222−4i4i000011-1-12i2i−2i−2i00000000−i−iii000000000000000000000000
χ574-44i−4i44-2-4-424i−4i4i−4i−2i2i4-2-2-4224i−4i−2i2i−2i2i000000-22−2i2i0000000000000000000000000000000000000000
χ584-44i−4i4-24-42-44i−4i−2i2i4i−4i-24-22-42−2i2i4i−4i−2i2i000000-22−2i2i0000000000000000000000000000000000000000
χ594-44i−4i4-2-2-4224i−4i−2i2i−2i2i-2-2122-1−2i2i−2i2ii−i0000001-1i−i000000000000000000003ζ3−3ζ33ζ−3ζ0000000000000000
χ604-44i−4i4-2-2-4224i−4i−2i2i−2i2i-2-2122-1−2i2i−2i2ii−i0000001-1i−i00000000000000000000−3ζ33ζ3−3ζ3ζ0000000000000000
χ614-44i−4i-2442-4-4−2i2i4i−4i4i−4i-2-2422-4−2i2i−2i2i4i−4i000000-22−2i2i0000000000000000000000000000000000000000
χ624-44i−4i-24-22-42−2i2i4i−4i−2i2i-21-22-12−2i2ii−i−2i2i0000001-1i−i00000000000000003ζ3−3ζ33ζ−3ζ00000000000000000000
χ634-44i−4i-24-22-42−2i2i4i−4i−2i2i-21-22-12−2i2ii−i−2i2i0000001-1i−i0000000000000000−3ζ33ζ3−3ζ3ζ00000000000000000000
χ644-44i−4i-2-2422-4−2i2i−2i2i4i−4i1-2-2-122i−i−2i2i−2i2i0000001-1i−i0000000000003ζ−3ζ3ζ3−3ζ3000000000000000000000000
χ654-44i−4i-2-2422-4−2i2i−2i2i4i−4i1-2-2-122i−i−2i2i−2i2i0000001-1i−i000000000000−3ζ3ζ−3ζ33ζ3000000000000000000000000
χ664-4−4i4i44-2-4-42−4i4i−4i4i2i−2i4-2-2-422−4i4i2i−2i2i−2i000000-222i−2i0000000000000000000000000000000000000000
χ674-4−4i4i4-24-42-4−4i4i2i−2i−4i4i-24-22-422i−2i−4i4i2i−2i000000-222i−2i0000000000000000000000000000000000000000
χ684-4−4i4i4-2-2-422−4i4i2i−2i2i−2i-2-2122-12i−2i2i−2i−ii0000001-1−ii000000000000000000003ζ−3ζ3ζ3−3ζ30000000000000000
χ694-4−4i4i4-2-2-422−4i4i2i−2i2i−2i-2-2122-12i−2i2i−2i−ii0000001-1−ii00000000000000000000−3ζ3ζ−3ζ33ζ30000000000000000
χ704-4−4i4i-2442-4-42i−2i−4i4i−4i4i-2-2422-42i−2i2i−2i−4i4i000000-222i−2i0000000000000000000000000000000000000000
χ714-4−4i4i-24-22-422i−2i−4i4i2i−2i-21-22-122i−2i−ii2i−2i0000001-1−ii00000000000000003ζ−3ζ3ζ3−3ζ300000000000000000000
χ724-4−4i4i-24-22-422i−2i−4i4i2i−2i-21-22-122i−2i−ii2i−2i0000001-1−ii0000000000000000−3ζ3ζ−3ζ33ζ300000000000000000000
χ734-4−4i4i-2-2422-42i−2i2i−2i−4i4i1-2-2-122−ii2i−2i2i−2i0000001-1−ii0000000000003ζ3−3ζ33ζ−3ζ000000000000000000000000
χ744-4−4i4i-2-2422-42i−2i2i−2i−4i4i1-2-2-122−ii2i−2i2i−2i0000001-1−ii000000000000−3ζ33ζ3−3ζ3ζ000000000000000000000000
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.