Finite Group Databasebeta

← Group #11723552

Character table — Group #11723552

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11222222222224444444444444444888888888888888812121212121212121212181818182424242436363636108108
order1233333466666233336666661212121212666666666666121212124824242424242424242412121212121246121248
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
χ51111111111111-11111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-111111111-11-1-11-1
χ61111111111111-11111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-11
χ71111111111111-11111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11111111111111-1-1-1-1-11-1-1-11
χ81111111111111-11111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1111111111-1-1-1-1-1-1-1-11-1111-1
χ92222222-22222202222002222-2-2-2-2-2000000000000-2-2-2-200000000002-2-2-20000020000
χ102222222-22222202222002222-2-2-2-2-2000000000000-2-2-2-20000000000-222200000-20000
χ11222222-122222-12-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1000000000022-1-100002-1-1-100
χ12222222-122222-12-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-10000000000-2-2110000-211100
χ13222222-122222-1-2-1-1-1-111-1-1-1-1-12222-2-2-2-211111111-1-1-1-1000000000022-1-10000-2-11100
χ14222222-122222-1-2-1-1-1-111-1-1-1-1-12222-2-2-2-211111111-1-1-1-10000000000-2-211000021-1-100
χ15222222-1-22222-10-1-1-1-1−i3i3-1-1-1-11-2-2-2-20000−i3−i3−i3−i3i3i3i3i3111100000000002-21100000-1−i3i300
χ16222222-1-22222-10-1-1-1-1−i3i3-1-1-1-11-2-2-2-20000−i3−i3−i3−i3i3i3i3i311110000000000-22-1-1000001i3−i300
χ17222222-1-22222-10-1-1-1-1i3−i3-1-1-1-11-2-2-2-20000i3i3i3i3−i3−i3−i3−i3111100000000002-21100000-1i3−i300
χ18222222-1-22222-10-1-1-1-1i3−i3-1-1-1-11-2-2-2-20000i3i3i3i3−i3−i3−i3−i311110000000000-22-1-1000001−i3i300
χ19222-1-1-1222-1-1-1222-1-1-1222-1-1-122-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-100002-1-1-1000000
χ20222-1-1-1222-1-1-1222-1-1-1222-1-1-122-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-2-2-2-21111110000-2111000000
χ21222-1-1-1222-1-1-12-22-1-1-1-2-22-1-1-122-1-1-1-2111-2111-21112-1-1-12-2-2-211111100002-1-1-1000000
χ22222-1-1-1222-1-1-12-22-1-1-1-2-22-1-1-122-1-1-1-2111-2111-21112-1-1-1-2222-1-1-1-1-1-10000-2111000000
χ2322-12-1-122-12-1-122-12-1-122-12-1-12-12-1-1-12-1-1-12-1-1-12-1-1-12-1-122-1-122-1-1-1-10000-12-1-1000000
χ2422-12-1-122-12-1-122-12-1-122-12-1-12-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-2-211-2-2111100001-211000000
χ2522-12-1-122-12-1-12-2-12-1-1-2-2-12-1-12-12-1-11-2111-2111-211-12-1-12-211-2-211110000-12-1-1000000
χ2622-12-1-122-12-1-12-2-12-1-1-2-2-12-1-12-12-1-11-2111-2111-211-12-1-1-22-1-122-1-1-1-100001-211000000
χ2722-1-12-122-1-12-122-1-12-122-1-12-12-1-12-1-1-12-1-1-12-1-1-12-1-1-12-122-1-1-1-122-1-10000-1-12-1000000
χ2822-1-12-122-1-12-122-1-12-122-1-12-12-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-2-21111-2-211000011-21000000
χ2922-1-12-122-1-12-12-2-1-12-1-2-2-1-12-12-1-12-111-2111-2111-21-1-12-12-21111-2-2110000-1-12-1000000
χ3022-1-12-122-1-12-12-2-1-12-1-2-2-1-12-12-1-12-111-2111-2111-21-1-12-1-22-1-1-1-122-1-1000011-21000000
χ3122-1-1-1222-1-1-1222-1-1-1222-1-1-122-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1222-1-1-1-1-1-1220000-1-1-12000000
χ3222-1-1-1222-1-1-1222-1-1-1222-1-1-122-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-2-2111111-2-20000111-2000000
χ3322-1-1-1222-1-1-122-2-1-1-12-2-2-1-1-122-1-1-12111-2111-2111-2-1-1-122-2111111-2-20000-1-1-12000000
χ3422-1-1-1222-1-1-122-2-1-1-12-2-2-1-1-122-1-1-12111-2111-2111-2-1-1-12-22-1-1-1-1-1-1220000111-2000000
χ35444-2-2-24-44-2-2-2404-2-2-2004-2-2-2-4-4222000000000000-4222000000000000000000000000
χ36444-2-2-2-244-2-2-2-24-2111-2-2-2111-24-2-2-24-2-2-2-2111-2111-2111000000000000000000000000
χ37444-2-2-2-244-2-2-2-2-4-211122-2111-24-2-2-2-42222-1-1-12-1-1-1-2111000000000000000000000000
χ38444-2-2-2-2-44-2-2-2-20-2111−2i32i3-21112-42220000−2i3i3i3i32i3−i3−i3−i32-1-1-1000000000000000000000000
χ39444-2-2-2-2-44-2-2-2-20-21112i3−2i3-21112-422200002i3−i3−i3−i3−2i3i3i3i32-1-1-1000000000000000000000000
χ4044-24-2-24-4-24-2-240-24-2-200-24-2-2-42-4220000000000002-422000000000000000000000000
χ4144-24-2-2-24-24-2-2-241-211-2-21-211-2-24-2-2-24-2-21-2111-2111-211000000000000000000000000
χ4244-24-2-2-24-24-2-2-2-41-211221-211-2-24-2-22-422-12-1-1-12-1-11-211000000000000000000000000
χ4344-24-2-2-2-4-24-2-2-201-211−2i32i31-21122-4220000i3−2i3i3i3−i32i3−i3−i3-12-1-1000000000000000000000000
χ4444-24-2-2-2-4-24-2-2-201-2112i3−2i31-21122-4220000−i32i3−i3−i3i3−2i3i3i3-12-1-1000000000000000000000000
χ4544-2-24-24-4-2-24-240-2-24-200-2-24-2-422-4200000000000022-42000000000000000000000000
χ4644-2-24-2-24-2-24-2-2411-21-2-211-21-2-2-24-2-2-24-211-2111-2111-21000000000000000000000000
χ4744-2-24-2-24-2-24-2-2-411-212211-21-2-2-24-222-42-1-12-1-1-12-111-21000000000000000000000000
χ4844-2-24-2-2-4-2-24-2-2011-21−2i32i311-21222-420000i3i3−2i3i3−i3−i32i3−i3-1-12-1000000000000000000000000
χ4944-2-24-2-2-4-2-24-2-2011-212i3−2i311-21222-420000−i3−i32i3−i3i3i3−2i3i3-1-12-1000000000000000000000000
χ5044-2-2-244-4-2-2-2440-2-2-2400-2-2-24-4222-4000000000000222-4000000000000000000000000
χ5144-2-2-24-24-2-2-24-24111-2-2-2111-2-2-2-2-24-2-2-24111-2111-2111-2000000000000000000000000
χ5244-2-2-24-24-2-2-24-2-4111-222111-2-2-2-2-24222-4-1-1-12-1-1-12111-2000000000000000000000000
χ5344-2-2-24-2-4-2-2-24-20111-2−2i32i3111-22222-40000i3i3i3−2i3−i3−i3−i32i3-1-1-12000000000000000000000000
χ5444-2-2-24-2-4-2-2-24-20111-22i3−2i3111-22222-40000−i3−i3−i32i3i3i3i3−2i3-1-1-12000000000000000000000000
χ554-4444440-4-4-4-4-40444400-4-4-4-4000000000000000000000000000000000000000000000
χ564-44444-20-4-4-4-420-2-2-2-200222200000000000000000000000000000000023−230000000000
χ574-44444-20-4-4-4-420-2-2-2-2002222000000000000000000000000000000000−23230000000000
χ584-44-2-2-240-4222-404-2-2-200-422200000000000000000000000006−66−66−600000000000000
χ594-44-2-2-240-4222-404-2-2-200-42220000000000000000000000000−66−66−6600000000000000
χ604-4-24-2-2402-422-40-24-2-2002-422000000000000000000000006−6006−6−6600000000000000
χ614-4-24-2-2402-422-40-24-2-2002-42200000000000000000000000−6600−666−600000000000000
χ624-4-2-24-24022-42-40-2-24-20022-42000000000000000000000006−6−66006−600000000000000
χ634-4-2-24-24022-42-40-2-24-20022-4200000000000000000000000−666−600−6600000000000000
χ644-4-2-2-2440222-4-40-2-2-2400222-4000000000000000000000006−66−6−660000000000000000
χ654-4-2-2-2440222-4-40-2-2-2400222-400000000000000000000000−66−666−60000000000000000
χ668-88-4-4-4-40-844440-4222004-2-2-2000000000000000000000000000000000000000000000
χ678-8-48-4-4-404-844402-42200-24-2-2000000000000000000000000000000000000000000000
χ688-8-4-48-4-4044-844022-4200-2-24-2000000000000000000000000000000000000000000000
χ698-8-4-4-48-40444-840222-400-2-2-24000000000000000000000000000000000000000000000

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