Finite Group Databasebeta

← Group #11722956

Character table — Group #11722956

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222224444444444446666666666668888121212121212121212121212121212121212121212181818181818363636363636108
order1222333666666666333666666666224466661212121236662666666666666661212121212124412121212246612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1
χ4111111111111111111111111111111-1-11111-1-1-1-11111-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11
χ51111111111111111111111111111-1-111-1-1-1-1111111111-1-11111-1-1-1-11111111111-1-1-1-1-1-11-111-1-1-1
χ61111111111111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11-1-1111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
χ9222222-12222-1-1-122-12-1-1-1222-1-1-1-1002200002222-1-1-1-120022-1-10000-1-1-1-1-1-1-1-1-1-100000020-1-1000
χ10222222-12222-1-1-122-12-1-1-1222-1-1-1-1002200002222-1-1-1-1-200-2-21100001111-1-1-1-1-1-1000000-2011000
χ11222222-12222-1-1-122-12-1-1-1222-1-1-1-100-2-20000-2-2-2-2-1-1-1-120022-1-10000-1-1-1-1111111000000-2011000
χ12222222-12222-1-1-122-12-1-1-1222-1-1-1-100-2-20000-2-2-2-2-1-1-1-1-200-2-2110000111111111100000020-1-1000
χ1322222-1222-1-1222-122-1-122-1-1-1-1-1-12220022220000-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-10000000000000200-1-10
χ1422222-1222-1-1222-122-1-122-1-1-1-1-1-12220022220000-1-1-1-1-2-1-111-2-2-1-1-1-111110000000000000-200110
χ1522222-1222-1-1222-122-1-122-1-1-1-1-1-12-2-200-2-2-2-20000-1-1-1-1211-1-1221111-1-1-1-10000000000000-200110
χ1622222-1222-1-1222-122-1-122-1-1-1-1-1-12-2-200-2-2-2-20000-1-1-1-1-21111-2-2111111110000000000000200-1-10
χ172222-122-1-1222222-1-1-12-1-1-1-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-10220000-1-1-1-1000022-1-1-1-122-1-1-1-10000000
χ182222-122-1-1222222-1-1-12-1-1-1-1-1222-122-2-2-1-1-1-11111-1-1-1-10220000-1-1-1-10000-2-21111-2-211110000000
χ192222-122-1-1222222-1-1-12-1-1-1-1-1222-1-2-2221111-1-1-1-1-1-1-1-10-2-200001111000022-1-1-1-1-2-211110000000
χ202222-122-1-1222222-1-1-12-1-1-1-1-1222-1-2-2-2-211111111-1-1-1-10-2-2000011110000-2-2111122-1-1-1-10000000
χ2122-2-22222-22-22-2-2-2-22222-22-2-22-2-2-200000000000022-2-20000000000000000000002i−2i2i2i−2i−2i0000000
χ2222-2-22222-22-22-2-2-2-22222-22-2-22-2-2-200000000000022-2-2000000000000000000000−2i2i−2i−2i2i2i0000000
χ2322-2-2-122-112-22-2-2-21-1-12-11-1112-2-210000−i3−i3i3i333−3−3-1-1110000000−i3−i3i3i300000033−3−32i−2i−i−iii0000000
χ2422-2-2-122-112-22-2-2-21-1-12-11-1112-2-210000−i3−i3i3i3−3−333-1-1110000000−i3−i3i3i3000000−3−333−2i2iii−i−i0000000
χ2522-2-2-122-112-22-2-2-21-1-12-11-1112-2-210000i3i3−i3−i333−3−3-1-1110000000i3i3−i3−i300000033−3−3−2i2iii−i−i0000000
χ2622-2-2-122-112-22-2-2-21-1-12-11-1112-2-210000i3i3−i3−i3−3−333-1-1110000000i3i3−i3−i3000000−3−3332i−2i−i−iii0000000
χ272-22-2222-2-2-22-2-22-22222-2-2-22-2-22-22002-200002-22-22-22-20000000000000002-22-22-20000000000000
χ282-22-2222-2-2-22-2-22-22222-2-2-22-2-22-2200-220000-22-222-22-2000000000000000-22-22-220000000000000
χ292-22-222-1-2-2-2211-1-22-12-111-22-21-11-1002-200002-22-2-11-1100000−i3i30000−i3−i3i3i3-11-11-1100000000−i3i3000
χ302-22-222-1-2-2-2211-1-22-12-111-22-21-11-1002-200002-22-2-11-1100000i3−i30000i3i3−i3−i3-11-11-1100000000i3−i3000
χ312-22-222-1-2-2-2211-1-22-12-111-22-21-11-100-220000-22-22-11-1100000−i3i30000−i3−i3i3i31-11-11-100000000i3−i3000
χ322-22-222-1-2-2-2211-1-22-12-111-22-21-11-100-220000-22-22-11-1100000i3−i30000i3i3−i3−i31-11-11-100000000−i3i3000
χ332-22-2-12211-22-2-22-2-1-1-12111-11-22-2-1002-2−i3i3−i3i3-11-11-11-110000000−i3i3−i3i300002-2-11-1100−i3i3−i3i30000000
χ342-22-2-12211-22-2-22-2-1-1-12111-11-22-2-1002-2i3−i3i3−i3-11-11-11-110000000i3−i3i3−i300002-2-11-1100i3−i3i3−i30000000
χ352-22-2-12211-22-2-22-2-1-1-12111-11-22-2-100-22−i3i3−i3i31-11-1-11-110000000−i3i3−i3i30000-221-11-100i3−i3i3−i30000000
χ362-22-2-12211-22-2-22-2-1-1-12111-11-22-2-100-22i3−i3i3−i31-11-1-11-110000000i3−i3i3−i30000-221-11-100−i3i3−i3i30000000
χ372-2-22222-22-2-2-22-22-2222-22-2-22-2-22-22-2002-2-2200002-2-2202-200002-2-2200000000000000000000000
χ382-2-22222-22-2-2-22-22-2222-22-2-22-2-22-2-2200-222-200002-2-220-220000-222-200000000000000000000000
χ392-2-222-12-2211-22-2-1-22-1-1-2211-111-1-22-2002-2-220000-111-10-11−i3i300-111-1−i3i3−i3i30000000000000000−i3i30
χ402-2-222-12-2211-22-2-1-22-1-1-2211-111-1-22-2002-2-220000-111-10-11i3−i300-111-1i3−i3i3−i30000000000000000i3−i30
χ412-2-222-12-2211-22-2-1-22-1-1-2211-111-1-2-2200-222-20000-111-101-1−i3i3001-1-11−i3i3−i3i30000000000000000i3−i30
χ422-2-222-12-2211-22-2-1-22-1-1-2211-111-1-2-2200-222-20000-111-101-1i3−i3001-1-11i3−i3i3−i30000000000000000−i3i30
χ432-2-22-1221-1-2-2-22-221-1-121-111-1-2-2212-200-111-13−3−33-111-102-20000-111-10000003−3−33003−3−330000000
χ442-2-22-1221-1-2-2-22-221-1-121-111-1-2-2212-200-111-1−333−3-111-102-20000-111-1000000−333−300−333−30000000
χ452-2-22-1221-1-2-2-22-221-1-121-111-1-2-221-22001-1-113−3−33-111-10-2200001-1-110000003−3−3300−333−30000000
χ462-2-22-1221-1-2-2-22-221-1-121-111-1-2-221-22001-1-11−333−3-111-10-2200001-1-11000000−333−3003−3−330000000
χ4744444-2-244-2-2-2-2-2-24-2-21-2-2-2-2-2111-20000000000001111400-2-2-2-2000011110000000000000000000
χ4844444-2-244-2-2-2-2-2-24-2-21-2-2-2-2-2111-20000000000001111-40022220000-1-1-1-10000000000000000000
χ494444-24-2-2-244-2-2-24-21-2-211-2-2-2-2-2-2100440000-2-2-2-21111000000000000000-2-211110000000000000
χ504444-24-2-2-244-2-2-24-21-2-211-2-2-2-2-2-2100-4-400002222111100000000000000022-1-1-1-10000000000000
χ514444-2-24-2-2-2-2444-2-2-21-2-2-2111-2-2-2-24400-2-2-2-2000011110-2-20000111100000000000000000000000
χ524444-2-24-2-2-2-2444-2-2-21-2-2-2111-2-2-2-2-4-4002222000011110220000-1-1-1-100000000000000000000000
χ5344-4-444-24-44-4-222-4-4-24-2-224-4-4-2222000000000000-2-2220000000000000000000000000000000000
χ5444-4-44-244-4-224-4-42-44-2-24-4-222-222-4000000000000-2-2220000000000000000000000000000000000
χ5544-4-44-2-24-4-22-2222-4-2-21-22-2221-1-1200000000000011-1-1000000000003-3-330000000000000000000
χ5644-4-44-2-24-4-22-2222-4-2-21-22-2221-1-1200000000000011-1-100000000000-333-30000000000000000000
χ5744-4-4-24-2-224-4-222-421-2-21-1-222-222-1000000002323−23−2311-1-100000000000000000−3−3330000000000000
χ5844-4-4-24-2-224-4-222-421-2-21-1-222-222-100000000−23−23232311-1-10000000000000000033−3−30000000000000
χ5944-4-4-2-24-22-224-4-422-21-2-221-1-1-22220000−2i3−2i32i32i3000011-1-10000000i3i3−i3−i300000000000000000000000
χ6044-4-4-2-24-22-224-4-422-21-2-221-1-1-222200002i32i3−2i3−2i3000011-1-10000000−i3−i3i3i300000000000000000000000
χ614-44-44-24-4-42-2-4-44244-2-2-4-42-222-224000000000000-22-220000000000000000000000000000000000
χ624-44-44-2-2-4-42-222-224-2-21222-22-11-1-20000000000001-11-100000−2i32i30000i3i3−i3−i30000000000000000000
χ634-44-44-2-2-4-42-222-224-2-21222-22-11-1-20000000000001-11-1000002i3−2i30000−i3−i3i3i30000000000000000000
χ644-44-4-24-222-4422-2-4-21-2-2-1-12-222-221004-40000-22-221-11-1000000000000000-221-11-10000000000000
χ654-44-4-24-222-4422-2-4-21-2-2-1-12-222-22100-4400002-22-21-11-10000000000000002-2-11-110000000000000
χ664-44-4-2-24222-2-4-442-2-21-222-11-12-22-20000−2i32i3−2i32i300001-11-10000000i3−i3i3−i300000000000000000000000
χ674-44-4-2-24222-2-4-442-2-21-222-11-12-22-200002i3−2i32i3−2i300001-11-10000000−i3i3−i3i300000000000000000000000
χ684-4-4444-2-44-4-42-224-4-24-22-2-4-4422-22000000000000-222-20000000000000000000000000000000000
χ694-4-444-2-2-44222-22-2-4-2-212-222-2-1-1120000000000001-1-11000−2i32i3000000i3−i3i3−i30000000000000000000
χ704-4-444-2-2-44222-22-2-4-2-212-222-2-1-1120000000000001-1-110002i3−2i3000000−i3i3−i3i30000000000000000000
χ714-4-44-24-22-2-4-42-22421-2-2-1122-222-2-10000000023−23−23231-1-1100000000000000000−333−30000000000000
χ724-4-44-24-22-2-4-42-22421-2-2-1122-222-2-100000000−232323−231-1-11000000000000000003−3−330000000000000
χ734-4-44-2-242-222-44-4-22-21-22-2-1-1122-224-400-222-200001-1-110-2200001-1-1100000000000000000000000
χ744-4-44-2-242-222-44-4-22-21-22-2-1-1122-22-44002-2-2200001-1-1102-20000-111-100000000000000000000000
χ758888-4-4-4-4-4-4-4-4-4-4-4-4222222222222000000000000-1-1-1-10000000000000000000000000000000000
χ7688-8-8-4-4-4-44-44-444442222-22-2-22-2-2-2000000000000-1-1110000000000000000000000000000000000
χ778-88-8-4-4-4444-444-44-4222-2-2-22-2-22-22000000000000-11-110000000000000000000000000000000000
χ788-8-88-4-4-44-4444-44-44222-22-2-22-2-22-2000000000000-111-10000000000000000000000000000000000

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