Finite Group Databasebeta

← Group #11723584

Character table — Group #11723584

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11222222222224444444444444444888888888888888812121212121212121212181818182424242436363636108108
order1233333466666333346666121212121212121212121212121212121212121212121228242424242424242424666666412121248
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ511111111111111111-111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-111111111-11-1-11-1
χ611111111111111111-111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-11
χ711111111111111111-111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-11-1-1-11
χ811111111111111111-111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1111-1
χ92222222-222222222202222-200-2-2-2-20000-2-2-2-20000000000000000002-22200000-20000
χ102222222-222222222202222-200-2-2-2-20000-2-2-2-2000000000000000000-22-2-20000020000
χ11222222-122222-1-1-1-1-12-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1000000000022-1-100002-1-1-100
χ12222222-122222-1-1-1-1-12-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-10000000000-2-2110000-211100
χ13222222-122222-1-1-1-1-1-2-1-1-1-1-1112222-2-2-2-2-1-1-1-111111111000000000022-1-10000-2-11100
χ14222222-122222-1-1-1-1-1-2-1-1-1-1-1112222-2-2-2-2-1-1-1-1111111110000000000-2-211000021-1-100
χ15222222-1-22222-1-1-1-1-10-1-1-1-11−i3i3-2-2-2-200001111−i3−i3−i3−i3i3i3i3i300000000002-2-1-1000001−i3i300
χ16222222-1-22222-1-1-1-1-10-1-1-1-11−i3i3-2-2-2-200001111−i3−i3−i3−i3i3i3i3i30000000000-221100000-1i3−i300
χ17222222-1-22222-1-1-1-1-10-1-1-1-11i3−i3-2-2-2-200001111i3i3i3i3−i3−i3−i3−i300000000002-2-1-1000001i3−i300
χ18222222-1-22222-1-1-1-1-10-1-1-1-11i3−i3-2-2-2-200001111i3i3i3i3−i3−i3−i3−i30000000000-221100000-1−i3i300
χ19222-1-1-1222-1-1-122-1-1-122-1-1-12222-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-100002-1-1-1000000
χ20222-1-1-1222-1-1-122-1-1-122-1-1-12222-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-2-2-2-21111110000-2111000000
χ21222-1-1-1222-1-1-122-1-1-1-22-1-1-12-2-22-1-1-1-21112-1-1-1-2111-21112-2-2-211111100002-1-1-1000000
χ22222-1-1-1222-1-1-122-1-1-1-22-1-1-12-2-22-1-1-1-21112-1-1-1-2111-2111-2222-1-1-1-1-1-10000-2111000000
χ2322-12-1-122-12-1-12-12-1-12-12-1-1222-12-1-1-12-1-1-12-1-1-12-1-1-12-1-122-1-122-1-1-1-10000-12-1-1000000
χ2422-12-1-122-12-1-12-12-1-12-12-1-1222-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-2-211-2-2111100001-211000000
χ2522-12-1-122-12-1-12-12-1-1-2-12-1-12-2-2-12-1-11-211-12-1-11-2111-2112-211-2-211110000-12-1-1000000
χ2622-12-1-122-12-1-12-12-1-1-2-12-1-12-2-2-12-1-11-211-12-1-11-2111-211-22-1-122-1-1-1-100001-211000000
χ2722-1-12-122-1-12-12-1-12-12-1-12-1222-1-12-1-1-12-1-1-12-1-1-12-1-1-12-122-1-1-1-122-1-10000-1-12-1000000
χ2822-1-12-122-1-12-12-1-12-12-1-12-1222-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-2-21111-2-211000011-21000000
χ2922-1-12-122-1-12-12-1-12-1-2-1-12-12-2-2-1-12-111-21-1-12-111-2111-212-21111-2-2110000-1-12-1000000
χ3022-1-12-122-1-12-12-1-12-1-2-1-12-12-2-2-1-12-111-21-1-12-111-2111-21-22-1-1-1-122-1-1000011-21000000
χ3122-1-1-1222-1-1-122-1-1-122-1-1-12222-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1222-1-1-1-1-1-1220000-1-1-12000000
χ3222-1-1-1222-1-1-122-1-1-122-1-1-12222-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-2-2111111-2-20000111-2000000
χ3322-1-1-1222-1-1-122-1-1-12-2-1-1-122-2-2-1-1-12111-2-1-1-12111-2111-22-2111111-2-20000-1-1-12000000
χ3422-1-1-1222-1-1-122-1-1-12-2-1-1-122-2-2-1-1-12111-2-1-1-12111-2111-2-22-1-1-1-1-1-1220000111-2000000
χ35444-2-2-24-44-2-2-244-2-2-204-2-2-2-400-42220000-422200000000000000000000000000000000
χ36444-2-2-2-244-2-2-2-2-21114-2111-2-2-24-2-2-24-2-2-2-2111-2111-2111000000000000000000000000
χ37444-2-2-2-244-2-2-2-2-2111-4-2111-2224-2-2-2-4222-21112-1-1-12-1-1-1000000000000000000000000
χ38444-2-2-2-2-44-2-2-2-2-21110-21112−2i32i3-422200002-1-1-1−2i3i3i3i32i3−i3−i3−i3000000000000000000000000
χ39444-2-2-2-2-44-2-2-2-2-21110-211122i3−2i3-422200002-1-1-12i3−i3−i3−i3−2i3i3i3i3000000000000000000000000
χ4044-24-2-24-4-24-2-24-24-2-20-24-2-2-4002-42200002-42200000000000000000000000000000000
χ4144-24-2-2-24-24-2-2-21-21141-211-2-2-2-24-2-2-24-2-21-2111-2111-211000000000000000000000000
χ4244-24-2-2-24-24-2-2-21-211-41-211-222-24-2-22-4221-211-12-1-1-12-1-1000000000000000000000000
χ4344-24-2-2-2-4-24-2-2-21-21101-2112−2i32i32-4220000-12-1-1i3−2i3i3i3−i32i3−i3−i3000000000000000000000000
χ4444-24-2-2-2-4-24-2-2-21-21101-21122i3−2i32-4220000-12-1-1−i32i3−i3−i3i3−2i3i3i3000000000000000000000000
χ4544-2-24-24-4-2-24-24-2-24-20-2-24-2-40022-42000022-4200000000000000000000000000000000
χ4644-2-24-2-24-2-24-2-211-21411-21-2-2-2-2-24-2-2-24-211-2111-2111-21000000000000000000000000
χ4744-2-24-2-24-2-24-2-211-21-411-21-222-2-24-222-4211-21-1-12-1-1-12-1000000000000000000000000
χ4844-2-24-2-2-4-2-24-2-211-21011-212−2i32i322-420000-1-12-1i3i3−2i3i3−i3−i32i3−i3000000000000000000000000
χ4944-2-24-2-2-4-2-24-2-211-21011-2122i3−2i322-420000-1-12-1−i3−i32i3−i3i3i3−2i3i3000000000000000000000000
χ5044-2-2-244-4-2-2-244-2-2-240-2-2-24-400222-40000222-400000000000000000000000000000000
χ5144-2-2-24-24-2-2-24-2111-24111-2-2-2-2-2-2-24-2-2-24111-2111-2111-2000000000000000000000000
χ5244-2-2-24-24-2-2-24-2111-2-4111-2-222-2-2-24222-4111-2-1-1-12-1-1-12000000000000000000000000
χ5344-2-2-24-2-4-2-2-24-2111-20111-22−2i32i3222-40000-1-1-12i3i3i3−2i3−i3−i3−i32i3000000000000000000000000
χ5444-2-2-24-2-4-2-2-24-2111-20111-222i3−2i3222-40000-1-1-12−i3−i3−i32i3i3i3i3−2i3000000000000000000000000
χ554-4444440-4-4-4-4-444440-4-4-4-400000000000000000000000000000000000000000000000
χ564-44444-20-4-4-4-42-2-2-2-20222200000000000000000000000000000000000−2i32i30000000000
χ574-44444-20-4-4-4-42-2-2-2-202222000000000000000000000000000000000002i3−2i30000000000
χ584-44-2-2-240-4222-44-2-2-20-42220000000000000000000000000006−66−66−600000000000000
χ594-44-2-2-240-4222-44-2-2-20-4222000000000000000000000000000−66−66−6600000000000000
χ604-4-24-2-2402-422-4-24-2-202-42200000000000000000000000006−6006−6−6600000000000000
χ614-4-24-2-2402-422-4-24-2-202-4220000000000000000000000000−6600−666−600000000000000
χ624-4-2-24-24022-42-4-2-24-2022-4200000000000000000000000006−6−66006−600000000000000
χ634-4-2-24-24022-42-4-2-24-2022-420000000000000000000000000−666−600−6600000000000000
χ644-4-2-2-2440222-4-4-2-2-240222-400000000000000000000000006−66−6−660000000000000000
χ654-4-2-2-2440222-4-4-2-2-240222-40000000000000000000000000−66−666−60000000000000000
χ668-88-4-4-4-40-84444-422204-2-2-200000000000000000000000000000000000000000000000
χ678-8-48-4-4-404-84442-4220-24-2-200000000000000000000000000000000000000000000000
χ688-8-4-48-4-4044-84422-420-2-24-200000000000000000000000000000000000000000000000
χ698-8-4-4-48-40444-84222-40-2-2-2400000000000000000000000000000000000000000000000

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