Finite Group Databasebeta

← Group #11723345

Character table — Group #11723345

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1122222222222224444444444444444444444444444444444444444444444412122424242424242424272736365454547272
order12333334666668833336666121212121212121212121212122424242424242424242424242424242424242424242424242424441212121212121212442228866
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111
χ51111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1111-11-1-11-1
χ61111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-11-111-11
χ71111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-111-1-1-11
χ81111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-11-1-1111-1
χ92222222-2222220022222222-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000002200-20000
χ102222222-2222220022222222-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000-2-20020000
χ11222222-12-1222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022000-1-1
χ12222222-12-1222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-200011
χ13222222-12-12222-2-2-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111110000000000002-2000-11
χ14222222-12-12222-2-2-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111111000000000000-220001-1
χ15222-1-1-12222-1-1-1222-1-1-12-1-1-122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-12-1-1-1000000000
χ16222-1-1-12222-1-1-1222-1-1-12-1-1-122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2111-2111000000000
χ17222-1-1-12222-1-1-1-2-22-1-1-12-1-1-122-1-1-122-1-1-1-1-1-1-2-2111111-2-2-2-2-2-21111111111112-22-1-1-1-2111000000000
χ18222-1-1-12222-1-1-1-2-22-1-1-12-1-1-122-1-1-122-1-1-1-1-1-1-2-2111111-2-2-2-2-2-2111111111111-22-21112-1-1-1000000000
χ1922-12-1-1222-12-1-122-12-1-1-12-1-12-12-1-1-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-12-1-1-12-1-1000000000
χ2022-12-1-1222-12-1-122-12-1-1-12-1-12-12-1-1-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-21-2111-211000000000
χ2122-12-1-1222-12-1-1-2-2-12-1-1-12-1-12-12-1-1-1-122-1-1-1-111-2-21111-2-21111-2-2-2-2111111112-2-12-1-11-211000000000
χ2222-12-1-1222-12-1-1-2-2-12-1-1-12-1-12-12-1-1-1-122-1-1-1-111-2-21111-2-21111-2-2-2-211111111-221-211-12-1-1000000000
χ2322-1-12-1222-1-12-122-1-12-1-1-12-12-1-12-1-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-122-1-12-1-1-12-1000000000
χ2422-1-12-1222-1-12-122-1-12-1-1-12-12-1-12-1-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-2-211-2111-21000000000
χ2522-1-12-1222-1-12-1-2-2-1-12-1-1-12-12-1-12-1-1-1-1-122-1-11111-2-211-2-211111111-2-2-2-211112-2-1-12-111-21000000000
χ2622-1-12-1222-1-12-1-2-2-1-12-1-1-12-12-1-12-1-1-1-1-122-1-11111-2-211-2-211111111-2-2-2-21111-2211-21-1-12-1000000000
χ2722-1-1-12222-1-1-1222-1-1-12-1-1-122-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-12-1-1-12000000000
χ2822-1-1-12222-1-1-1222-1-1-12-1-1-122-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-2-2111-2111-2000000000
χ2922-1-1-12222-1-1-12-2-2-1-1-12-1-1-122-1-1-12-1-1-1-1-1-122111111-2-2-2-2111111111111-2-2-2-22-2-1-1-12111-2000000000
χ3022-1-1-12222-1-1-12-2-2-1-1-12-1-1-122-1-1-12-1-1-1-1-1-122111111-2-2-2-2111111111111-2-2-2-2-22111-2-1-1-12000000000
χ312-2222220-2-2-2-2-22−22222-2-2-2-200000000000002−22−22−22−22−222−2−222−2−222−2−222−2−200000000002i−2i000i2−i200
χ322-2222220-2-2-2-2-22−22222-2-2-2-200000000000002−22−22−22−22−222−2−222−2−222−2−222−2−20000000000−2i2i000−i2i200
χ332-2222220-2-2-2-2-2−222222-2-2-2-20000000000000−22−22−22−22−22−2−222−2−222−2−222−2−22200000000002i−2i000−i2i200
χ342-2222220-2-2-2-2-2−222222-2-2-2-20000000000000−22−22−22−22−22−2−222−2−222−2−222−2−2220000000000−2i2i000i2−i200
χ35444444-2-4-2444400-2-2-2-2-2-2-2-22-4-4-4-422222222000000000000000000000000000000000000000000000
χ36444-2-2-24-444-2-2-2004-2-2-24-2-2-2-4-4222-4-4222222000000000000000000000000000000000000000000000
χ37444-2-2-2-24-24-2-2-244-2111-2111-24-2-2-2-2-211111144-2-2-2-2-2-2-2-2-2-2-2-21111111111110000000000000000000
χ38444-2-2-2-24-24-2-2-2-4-4-2111-2111-24-2-2-2-2-2111111-4-4222222222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000
χ39444-2-2-2-2-4-24-2-2-200-2111-21112-422222-1-1-1-1-1-1000000000000003i−3i3i−3i3i−3i3i−3i3i−3i3i−3i0000000000000000000
χ40444-2-2-2-2-4-24-2-2-200-2111-21112-422222-1-1-1-1-1-100000000000000−3i3i−3i3i−3i3i−3i3i−3i3i−3i3i0000000000000000000
χ4144-24-2-24-44-24-2-200-24-2-2-24-2-2-42-42222-4-42222000000000000000000000000000000000000000000000
χ4244-24-2-2-24-2-24-2-2441-2111-211-2-24-2-211-2-21111-2-244-2-2-2-2-2-21111-2-2-2-2111111110000000000000000000
χ4344-24-2-2-24-2-24-2-2-4-41-2111-211-2-24-2-211-2-2111122-4-4222222-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000000
χ4444-24-2-2-2-4-2-24-2-2001-2111-21122-422-1-122-1-1-1-100000000003i−3i3i−3i00003i−3i3i−3i−3i3i−3i3i0000000000000000000
χ4544-24-2-2-2-4-2-24-2-2001-2111-21122-422-1-122-1-1-1-10000000000−3i3i−3i3i0000−3i3i−3i3i3i−3i3i−3i0000000000000000000
χ4644-2-24-24-44-2-24-200-2-24-2-2-24-2-422-422222-4-422000000000000000000000000000000000000000000000
χ4744-2-24-2-24-2-2-24-24411-2111-21-2-2-24-21111-2-211-2-2-2-244-2-2-2-211111111-2-2-2-211110000000000000000000
χ4844-2-24-2-24-2-2-24-2-4-411-2111-21-2-2-24-21111-2-2112222-4-42222-1-1-1-1-1-1-1-12222-1-1-1-10000000000000000000
χ4944-2-24-2-2-4-2-2-24-20011-2111-21222-42-1-1-1-122-1-100000000003i−3i3i−3i−3i3i−3i3i00003i−3i3i−3i0000000000000000000
χ5044-2-24-2-2-4-2-2-24-20011-2111-21222-42-1-1-1-122-1-10000000000−3i3i−3i3i3i−3i3i−3i0000−3i3i−3i3i0000000000000000000
χ5144-2-2-244-44-2-2-2400-2-2-24-2-2-24-4222-4222222-4-4000000000000000000000000000000000000000000000
χ5244-2-2-24-24-2-2-2-2444111-2111-2-2-2-2-24111111-2-2-2-2-2-2-2-244-2-2111111111111-2-2-2-20000000000000000000
χ5344-2-2-24-24-2-2-2-24-4-4111-2111-2-2-2-2-24111111-2-2222222-4-422-1-1-1-1-1-1-1-1-1-1-1-122220000000000000000000
χ5444-2-2-24-2-4-2-2-2-2400111-2111-22222-4-1-1-1-1-1-12200000000003i−3i3i−3i3i−3i3i−3i−3i3i−3i3i00000000000000000000000
χ5544-2-2-24-2-4-2-2-2-2400111-2111-22222-4-1-1-1-1-1-1220000000000−3i3i−3i3i−3i3i−3i3i3i−3i3i−3i00000000000000000000000
χ564-44444-202-4-4-4-422−22-2-2-2-22222000000000000022−2222−2222−2222−22−22−2−222−2−222−2−222−2−2220000000000000000000
χ574-44444-202-4-4-4-4−2222-2-2-2-222220000000000000−2222−2222−2222−22222−222−2−222−2−222−2−222−2−20000000000000000000
χ584-44-2-2-240-4-422222−224-2-2-2-4222000000000000022−22−22−22−2222−222222−22−22−2−222−2−222−2−2220000000000000000000
χ594-44-2-2-240-4-4222−22224-2-2-2-42220000000000000−22222−22−22−2−2222−22−22222222−2−222−2−222−2−20000000000000000000
χ604-44-2-2-2-202-422222−22-21112-1-1-100000003i−3i3i−3i3i−3i22−22−22−22−22−22−2−2222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ30000000000000000000
χ614-44-2-2-2-202-422222−22-21112-1-1-10000000−3i3i−3i3i−3i3i22−22−22−22−22−22−2−222−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ30000000000000000000
χ624-44-2-2-2-202-4222−2222-21112-1-1-100000003i−3i3i−3i3i−3i−22222−22−22−22−222−2−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ30000000000000000000
χ634-44-2-2-2-202-4222−2222-21112-1-1-10000000−3i3i−3i3i−3i3i−22222−22−22−22−222−2−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ30000000000000000000
χ644-4-24-2-240-42-42222−22-24-2-22-4220000000000000−2222−22−22−2222−22−2−2222222−22−22−2−222−2−2220000000000000000000
χ654-4-24-2-240-42-422−2222-24-2-22-42200000000000002−2−22222−22−2−222222−2−2−22−22222222−2−222−2−20000000000000000000
χ664-4-24-2-2-2022-42222−221-211-12-1-1000003i−3i003i−3i−3i3i−2222−22−22−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−2−2222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ30000000000000000000
χ674-4-24-2-2-2022-42222−221-211-12-1-100000−3i3i00−3i3i3i−3i−2222−22−22−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−2−222−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ30000000000000000000
χ684-4-24-2-2-2022-422−22221-211-12-1-1000003i−3i003i−3i−3i3i2−2−22222−22−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ322−2−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ30000000000000000000
χ694-4-24-2-2-2022-422−22221-211-12-1-100000−3i3i00−3i3i3i−3i2−2−22222−22−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ322−2−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ30000000000000000000
χ704-4-2-24-240-422-4222−22-2-24-222-420000000000000−22−2222−22−2222−22−2−222−2−2222222−22−22−2−2220000000000000000000
χ714-4-2-24-240-422-42−2222-2-24-222-4200000000000002−22−2−22222−2−222222−2−222−2−2−22−22222222−2−20000000000000000000
χ724-4-2-24-2-20222-4222−2211-21-1-12-1000003i−3i−3i3i003i−3i−22−2222−22−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−2−2222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ30000000000000000000
χ734-4-2-24-2-20222-4222−2211-21-1-12-100000−3i3i3i−3i00−3i3i−22−2222−22−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−2−222−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ30000000000000000000
χ744-4-2-24-2-20222-42−222211-21-1-12-1000003i−3i−3i3i003i−3i2−22−2−22222−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ322−2−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ30000000000000000000
χ754-4-2-24-2-20222-42−222211-21-1-12-100000−3i3i3i−3i00−3i3i2−22−2−22222−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ322−2−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ30000000000000000000
χ764-4-2-2-2440-4222-422−22-2-2-24222-40000000000000−22−22−2222−2222−22−2−222−2−222−2−2222222−22−220000000000000000000
χ774-4-2-2-2440-4222-4−2222-2-2-24222-400000000000002−22−22−2−2222−222222−2−222−2−222−2−2−22−2222220000000000000000000
χ784-4-2-2-24-202222-422−22111-2-1-1-12000003i−3i3i−3i−3i3i00−22−22−2222−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−2−2220000000000000000000
χ794-4-2-2-24-202222-422−22111-2-1-1-1200000−3i3i−3i3i3i−3i00−22−22−2222−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−2−2220000000000000000000
χ804-4-2-2-24-202222-4−2222111-2-1-1-12000003i−3i3i−3i−3i3i002−22−22−2−22222−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ322−2−20000000000000000000
χ814-4-2-2-24-202222-4−2222111-2-1-1-1200000−3i3i−3i3i3i−3i002−22−22−2−22222−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ322−2−20000000000000000000

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