Finite Group Databasebeta

← Group #13156678

Character table — Group #13156678

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222244444444444444444488888888888888242424242424242424242424242424242424242424242424242424363636363636363636363636363636363636216
order1222333446666666663336666666661212121212123666121212121212121212124441212121212121212121212121212121212121212121212124488881212121224242424242424244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1111111-1-111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1111-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111
χ511111111111111111111111111111111111111111111111111-111-1-1111111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1
χ611111111111111111111111111111111111111111111111111-11-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11
χ711111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1
χ92222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-20000000000000000000000000002-2000022-2-2000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000-220000-2-222000000000
χ11222222-122222-1222-1-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-120222000022-1-1-1-1-1-1-1-10000-1-1-1-1220000-1-1-1-1000000000
χ12222222-122222-1222-1-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-120-2220000-2-2-1-111-1-1-1-100001111-2-200001111000000000
χ13222222-122222-1222-1-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1-202-2-200002211-1-111110000-1-1-1-1-2-200001111000000000
χ14222222-122222-1222-1-12-1-12-1-12-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1-20-2-2-20000-2-21111111100001111220000-1-1-1-1000000000
χ15222222-1-2-2222-1222-1-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111100000000000−i3i3−i3i3−i3−i3i3i30000−i3−i3i3i32-20000-1-111000000000
χ16222222-1-2-2222-1222-1-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111100000000000−i3i3i3−i3−i3−i3i3i30000i3i3−i3−i3-22000011-1-1000000000
χ17222222-1-2-2222-1222-1-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111100000000000i3−i3−i3i3i3i3−i3−i30000−i3−i3i3i3-22000011-1-1000000000
χ18222222-1-2-2222-1222-1-12-1-12-1-12-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111100000000000i3−i3i3−i3i3i3−i3−i30000i3i3−i3−i32-20000-1-111000000000
χ1922222-122222-12-1-1222-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1220-1-1-1-122002200-1-1-1-1-1-1-1-100000022000000-1-1-1-100000
χ2022222-122222-12-1-1222-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-12-20-1-111-2-2002200-1-1-1-11111000000-2-2000000111100000
χ2122222-122222-12-1-1222-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-22011-1-12200-2-2001111-1-1-1-1000000-2-2000000111100000
χ2222222-122222-12-1-1222-12-1-12-1-12-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-2-201111-2-200-2-2001111111100000022000000-1-1-1-100000
χ232222-12222-1-12222-122-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-10220022-1-1-1-100220000-1-1-1-1-1-1-1-100002200000000-1-1-1-10
χ242222-12222-1-12222-122-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-102-20022-1-11100-2-20000-1-1-1-111110000-2-20000000011110
χ252222-12222-1-12222-122-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-10-2200-2-211-1-1002200001111-1-1-1-10000-2-20000000011110
χ262222-12222-1-12222-122-1-12-1-12-1-12-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-10-2-200-2-2111100-2-200001111111100002200000000-1-1-1-10
χ2722-2-22222-2-2222-2-2-2-2-2222-2-2-2222-2-2-22-22-2-222-2-222-22-22-222-2-2000000000000000000000000000002-200000022-2-200000
χ2822-2-22222-2-2222-2-2-2-2-2222-2-2-2222-2-2-22-22-2-222-2-222-22-22-222-2-200000000000000000000000000000-22000000-2-22200000
χ2922-2-2222-22-2222-2-2-2-2-2222-2-2-2222-2-2-2-22-222-22-2-22-22-22-22-2-22200000000000000000000000000000002-20000000022-2-20
χ3022-2-2222-22-2222-2-2-2-2-2222-2-2-2222-2-2-2-22-222-22-2-22-22-22-22-2-2220000000000000000000000000000000-2200000000-2-2220
χ3122-2-22-122-2-22-1211-2-2-2-12-11-21-12-11-21212-2-2-1-111-1-112-2-11-1-1110003−33−3000000003−33−333−3−30000002-2000000-1-11100000
χ3222-2-22-122-2-22-1211-2-2-2-12-11-21-12-11-21212-2-2-1-111-1-112-2-11-1-1110003−3−33000000003−33−3−3−333000000-2200000011-1-100000
χ3322-2-22-122-2-22-1211-2-2-2-12-11-21-12-11-21212-2-2-1-111-1-112-2-11-1-111000−333−300000000−33−3333−3−3000000-2200000011-1-100000
χ3422-2-22-122-2-22-1211-2-2-2-12-11-21-12-11-21212-2-2-1-111-1-112-2-11-1-111000−33−3300000000−33−33−3−3330000002-2000000-1-11100000
χ3522-2-2-122-221-122-2-21-2-2-1-1211-2-1-1211-212-22-1-2-111-11-11-1-2211-1-100000003−33−3000000003−33−33−33−300002-200000000-1-1110
χ3622-2-2-122-221-122-2-21-2-2-1-1211-2-1-1211-212-22-1-2-111-11-11-1-2211-1-100000003−3−33000000003−33−3−33−330000-220000000011-1-10
χ3722-2-2-122-221-122-2-21-2-2-1-1211-2-1-1211-212-22-1-2-111-11-11-1-2211-1-10000000−333−300000000−33−333−33−30000-220000000011-1-10
χ3822-2-2-122-221-122-2-21-2-2-1-1211-2-1-1211-212-22-1-2-111-11-11-1-2211-1-10000000−33−3300000000−33−33−33−3300002-200000000-1-1110
χ3944444-24-4-444-24-2-2444-24-2-24-2-24-2-24-2-42-4-4-42-2-2-2-222-4-42222220000000000000000000000000000000000000000000000
χ4044444-2-24444-2-2-2-24-2-2-2-21-2-21-2-21-2-214-2-2-24-21111-2-2-2-2111111400-2-2000000-2-2001111000000000000000000000000000
χ4144444-2-24444-2-2-2-24-2-2-2-21-2-21-2-21-2-214-2-2-24-21111-2-2-2-2111111-400220000002200-1-1-1-1000000000000000000000000000
χ4244444-2-2-4-444-2-2-2-24-2-2-2-21-2-21-2-21-2-21-4222-4211112222-1-1-1-1-1-100000000000−2i32i300i3i3−i3−i3000000000000000000000000000
χ4344444-2-2-4-444-2-2-2-24-2-2-2-21-2-21-2-21-2-21-4222-4211112222-1-1-1-1-1-1000000000002i3−2i300−i3−i3i3i3000000000000000000000000000
χ444444-244-4-4-2-24444-244-2-24-2-24-2-24-2-242-4-4-42-4-2-2-2-22222-4-422220000000000000000000000000000000000000000000000
χ454444-24-244-2-24-244-2-2-2-21-2-21-2-21-2-21-2-24-2-2-241111-2-211-2-21111004000000-2-200-2-20000000011110000000000000000000
χ464444-24-244-2-24-244-2-2-2-21-2-21-2-21-2-21-2-24-2-2-241111-2-211-2-2111100-400000022002200000000-1-1-1-10000000000000000000
χ474444-24-2-4-4-2-24-244-2-2-2-21-2-21-2-21-2-21-22-4222-4111122-1-122-1-1-1-10000000000000−2i32i300000000i3i3−i3−i30000000000000000000
χ484444-24-2-4-4-2-24-244-2-2-2-21-2-21-2-21-2-21-22-4222-4111122-1-122-1-1-1-100000000000002i3−2i300000000−i3−i3i3i30000000000000000000
χ494444-2-2444-2-2-24-2-2-2441-2-21-2-21-2-21-2-2-2-244-2-2111111-2-2-2-2111104000-2-2-2-20000000000111100000000000000000000000
χ504444-2-2444-2-2-24-2-2-2441-2-21-2-21-2-21-2-2-2-244-2-2111111-2-2-2-211110-400022220000000000-1-1-1-100000000000000000000000
χ514444-2-24-4-4-2-2-24-2-2-2441-2-21-2-21-2-21-2-222-4-4221111-1-12222-1-1-1-100000000000000000003-3-3300000000000000000000000
χ524444-2-24-4-4-2-2-24-2-2-2441-2-21-2-21-2-21-2-222-4-4221111-1-12222-1-1-1-10000000000000000000-333-300000000000000000000000
χ5344-4-444-24-4-444-2-4-4-4224-2-2-4224-2-2-4224-4-22-44-222-24-4-22-22-2-2220000000000000000000000000000000000000000000000
χ5444-4-444-2-44-444-2-4-4-4224-2-2-4224-2-2-422-442-24-4-222-2-442-22-222-2-20000000000000000000000000000000000000000000000
χ5544-4-44-24-44-44-2422-4-4-4-24-22-42-24-22-42-4-2-4442-222-22-2-442-222-2-20000000000000000000000000000000000000000000000
χ5644-4-44-2-24-4-44-2-222-422-2-2122-1-2-2122-142-22-4-21-1-11-22-221-111-1-100023−230000000000−33−33000000000000000000000000000
χ5744-4-44-2-24-4-44-2-222-422-2-2122-1-2-2122-142-22-4-21-1-11-22-221-111-1-1000−232300000000003−33−3000000000000000000000000000
χ5844-4-44-2-2-44-44-2-222-422-2-2122-1-2-2122-1-4-22-2421-1-112-22-2-11-1-1110000000000000003i−3i−3i3i000000000000000000000000000
χ5944-4-44-2-2-44-44-2-222-422-2-2122-1-2-2122-1-4-22-2421-1-112-22-2-11-1-111000000000000000−3i3i3i−3i000000000000000000000000000
χ6044-4-4-2444-42-244-4-42-4-4-2-2422-4-2-2422-4-2-44-424-222-2-22-224-4-2-2220000000000000000000000000000000000000000000000
χ6144-4-4-24-24-42-24-2-4-4222-21-22-12-21-22-12-2-4-22241-1-11-221-1-2211-1-1000000000000000000000003i−3i−3i3i0000000000000000000
χ6244-4-4-24-24-42-24-2-4-4222-21-22-12-21-22-12-2-4-22241-1-11-221-1-2211-1-100000000000000000000000−3i3i3i−3i0000000000000000000
χ6344-4-4-24-2-442-24-2-4-4222-21-22-12-21-22-12242-2-2-41-1-112-2-112-2-1-11100000000023−23000000000000−33−330000000000000000000
χ6444-4-4-24-2-442-24-2-4-4222-21-22-12-21-22-12242-2-2-41-1-112-2-112-2-1-111000000000−23230000000000003−33−30000000000000000000
χ6544-4-4-2-244-42-2-24222-4-41-2-2-1221-2-2-122-224-42-21-1-111-1-22-2211-1-10000023−23000000000000−3−33300000000000000000000000
χ6644-4-4-2-244-42-2-24222-4-41-2-2-1221-2-2-122-224-42-21-1-111-1-22-2211-1-100000−232300000000000033−3−300000000000000000000000
χ6744-4-4-2-24-442-2-24222-4-41-2-2-1221-2-2-1222-2-44-221-1-11-112-22-2-1-111000000023−230000000000−33−3300000000000000000000000
χ6844-4-4-2-24-442-2-24222-4-41-2-2-1221-2-2-1222-2-44-221-1-11-112-22-2-1-1110000000−232300000000003−33−300000000000000000000000
χ694-44-4444004-4-4-44-4-44-444444-4-4-4-4-4-4400000044-4-400000000000000000000000000000000000000000000000000000000
χ704-44-444-2004-4-424-4-4-224-2-24-22-422-42-2000000-2-22200000000000000000000000000000000000000000000023−23000000000
χ714-44-444-2004-4-424-4-4-224-2-24-22-422-42-2000000-2-222000000000000000000000000000000000000000000000−2323000000000
χ724-44-44-24004-42-4-22-44-4-24-2-2422-422-4-2000000-2-222000000000000000000000000000000000000000000000006−66−600000
χ734-44-44-24004-42-4-22-44-4-24-2-2422-422-4-2000000-2-22200000000000000000000000000000000000000000000000−66−6600000
χ744-44-4-24400-22-4-44-424-4-2-24-2-2-422-4224000000-2-222000000000000000000000000000000000000000000000000000i6−i6i6−i60
χ754-44-4-24400-22-4-44-424-4-2-24-2-2-422-4224000000-2-222000000000000000000000000000000000000000000000000000−i6i6−i6i60
χ764-4-4444400-4-4-4-4-444-44444-4-44-4-4-444-40000004-44-400000000000000000000000000000000000000000000000000000000
χ774-4-4444-200-4-4-42-4442-24-2-2-42-2-4224-22000000-22-22000000000000000000000000000000000000000000023−2300000000000
χ784-4-4444-200-4-4-42-4442-24-2-2-42-2-4224-22000000-22-220000000000000000000000000000000000000000000−232300000000000
χ794-4-444-2400-4-42-42-24-44-24-22-4-22-42-242000000-22-22000000000000000000000000000000000000000000000006−6−6600000
χ804-4-444-2400-4-42-42-24-44-24-22-4-22-42-242000000-22-2200000000000000000000000000000000000000000000000−666−600000
χ814-4-44-2440022-4-4-44-2-44-2-2422422-4-2-2-4000000-22-22000000000000000000000000000000000000000000000000000i6−i6−i6i60
χ824-4-44-2440022-4-4-44-2-44-2-2422422-4-2-2-4000000-22-22000000000000000000000000000000000000000000000000000−i6i6i6−i60
χ838888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000
χ848888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000
χ8588-8-8-4-4-48-84-4-4-444444222-2-2-2222-2-2-2-44-444-4-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000
χ8688-8-8-4-4-4-884-4-4-444444222-2-2-2222-2-2-24-44-4-44-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000
χ878-88-88-4-4008-844-44-8-44-4-42-4-4-244-244200000022-2-200000000000000000000000000000000000000000000000000000000
χ888-88-8-48-400-44-848-84-44-42-4-4244-244-2-400000022-2-200000000000000000000000000000000000000000000000000000000
χ898-88-8-4-4800-444-8-4448-82-4-42-44-244-24-400000022-2-200000000000000000000000000000000000000000000000000000000
χ908-88-8-4-4-400-4444-444-4422222-2-2-2-2-2-22000000-1-11100000033−3333−330000000000000000000000000000000000000000000000
χ918-88-8-4-4-400-4444-444-4422222-2-2-2-2-2-22000000-1-111000000−3333−33330000000000000000000000000000000000000000000000
χ928-8-888-4-400-8-8444-484-4-4-4244244-2-4-4-20000002-22-200000000000000000000000000000000000000000000000000000000
χ938-8-88-48-40044-84-88-44-4-42-44-2-44-24-4240000002-22-200000000000000000000000000000000000000000000000000000000
χ948-8-88-4-4800444-84-4-4-882-4-4-24-4-2442-440000002-22-200000000000000000000000000000000000000000000000000000000
χ958-8-88-4-4-40044444-4-44-4222-2-22-2-2-222-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000
χ968-8-88-4-4-40044444-4-44-4222-2-22-2-2-222-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000

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