Finite Group Databasebeta

← Group #13156550

Character table — Group #13156550

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222244444444444444444488888888888888242424242424242424242424242424242424242424242424242424363636363636363636363636363636363636216
order12223334466666666633366666666612121212121236661212121212121212121224466666666121212121212121212121212121212124488881212121224242424242424244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-11111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111
χ511111111111111111111111111111111111111111111111111-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1
χ611111111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11
χ711111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11
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
χ11222222-122222222-1-1-12-1-12-1-1-1-12-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-122022-1-1-1-1-1-1000022-1-10000-1-1-1-1220000-1-1-1-1000000000
χ12222222-122222222-1-1-12-1-12-1-1-1-12-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-12-2022-1-1-1-1-1-10000-2-21100001111-2-200001111000000000
χ13222222-122222222-1-1-12-1-12-1-1-1-12-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1-220-2-2111111000022-1-10000-1-1-1-1-2-200001111000000000
χ14222222-122222222-1-1-12-1-12-1-1-1-12-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1-2-20-2-21111110000-2-21100001111220000-1-1-1-1000000000
χ15222222-1-2-2222222-1-1-12-1-12-1-1-1-12-12-1-2-211-2-2-1-1-1-1-2-21111111100000−i3i3−i3−i3i3i3000000−i3i30000−i3−i3i3i32-20000-1-111000000000
χ16222222-1-2-2222222-1-1-12-1-12-1-1-1-12-12-1-2-211-2-2-1-1-1-1-2-21111111100000−i3i3−i3−i3i3i3000000i3−i30000i3i3−i3−i3-22000011-1-1000000000
χ17222222-1-2-2222222-1-1-12-1-12-1-1-1-12-12-1-2-211-2-2-1-1-1-1-2-21111111100000i3−i3i3i3−i3−i3000000−i3i30000−i3−i3i3i3-22000011-1-1000000000
χ18222222-1-2-2222222-1-1-12-1-12-1-1-1-12-12-1-2-211-2-2-1-1-1-1-2-21111111100000i3−i3i3i3−i3−i3000000i3−i30000i3i3−i3−i32-20000-1-111000000000
χ1922222-12222-1-12-12222-12-1-122-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1202-1-122-1-1-1-122-1-10000-1-1-1-100000022000000-1-1-1-100000
χ2022222-12222-1-12-12222-12-1-122-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-120-2-1-122-1-1-1-1-2-21100001111000000-2-2000000111100000
χ2122222-12222-1-12-12222-12-1-122-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-20211-2-2111122-1-10000-1-1-1-1000000-2-2000000111100000
χ2222222-12222-1-12-12222-12-1-122-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-20-211-2-21111-2-2110000111100000022000000-1-1-1-100000
χ232222-12222-122-12-1222-1-12-1-1-122-12-1-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-102200000000-1-122-1-122-1-1-1-1-1-1-1-100002200000000-1-1-1-10
χ242222-12222-122-12-1222-1-12-1-1-122-12-1-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-102-20000000011-2-2-1-1221111-1-1-1-10000-2-20000000011110
χ252222-12222-122-12-1222-1-12-1-1-122-12-1-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-10-2200000000-1-12211-2-2-1-1-1-111110000-2-20000000011110
χ262222-12222-122-12-1222-1-12-1-1-122-12-1-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-10-2-20000000011-2-211-2-21111111100002200000000-1-1-1-10
χ2722-2-22222-2-2-22-2-222-2-2222-2-2-2-2-222-222-22-2-222-2-222-22-22-222-2-2000000000000000000000000000002i−2i0000002i2i−2i−2i00000
χ2822-2-22222-2-2-22-2-222-2-2222-2-2-2-2-222-222-22-2-222-2-222-22-22-222-2-200000000000000000000000000000−2i2i000000−2i−2i2i2i00000
χ2922-2-2222-22-2-22-2-222-2-2222-2-2-2-2-222-22-22-222-22-2-22-22-22-22-2-22200000000000000000000000000000002i−2i000000002i2i−2i−2i0
χ3022-2-2222-22-2-22-2-222-2-2222-2-2-2-2-222-22-22-222-22-2-22-22-22-22-2-2220000000000000000000000000000000−2i2i00000000−2i−2i2i2i0
χ3122-2-22-122-2-21-1-2122-2-2-12-11-2-211-1-112-1-22-212-111-1-11-112-2-1-111000−i3i300−i3i3−i3i3003−3000033−3−30000002i−2i000000−i−iii00000
χ3222-2-22-122-2-21-1-2122-2-2-12-11-2-211-1-112-1-22-212-111-1-11-112-2-1-111000−i3i300−i3i3−i3i300−330000−3−333000000−2i2i000000ii−i−i00000
χ3322-2-22-122-2-21-1-2122-2-2-12-11-2-211-1-112-1-22-212-111-1-11-112-2-1-111000i3−i300i3−i3i3−i3003−3000033−3−3000000−2i2i000000ii−i−i00000
χ3422-2-22-122-2-21-1-2122-2-2-12-11-2-211-1-112-1-22-212-111-1-11-112-2-1-111000i3−i300i3−i3i3−i300−330000−3−3330000002i−2i000000−i−iii00000
χ3522-2-2-122-221-221-2-12-2-2-1-12111-2-2-121-1-2-1-2221-111-11-1-221-111-1-1000000000003−300−i3i3003−33−3−i3i3−i3i300002i−2i00000000−i−iii0
χ3622-2-2-122-221-221-2-12-2-2-1-12111-2-2-121-1-2-1-2221-111-11-1-221-111-1-1000000000003−300i3−i3003−33−3i3−i3i3−i30000−2i2i00000000ii−i−i0
χ3722-2-2-122-221-221-2-12-2-2-1-12111-2-2-121-1-2-1-2221-111-11-1-221-111-1-100000000000−3300−i3i300−33−33−i3i3−i3i30000−2i2i00000000ii−i−i0
χ3822-2-2-122-221-221-2-12-2-2-1-12111-2-2-121-1-2-1-2221-111-11-1-221-111-1-100000000000−3300i3−i300−33−33i3−i3i3−i300002i−2i00000000−i−iii0
χ3944444-24-4-44-2-24-24444-24-2-244-2-2-2-2-242-4-4-42-4-2-2-2-22222-4-422220000000000000000000000000000000000000000000000
χ4044444-2-2444-2-24-24-2-2-2-2-21-2-2-211-21-2-2-24-2-2-241111-2-211-2-21111400-2-2-2-2111100000000000000000000000000000000000
χ4144444-2-2444-2-24-24-2-2-2-2-21-2-2-211-21-2-2-24-2-2-241111-2-211-2-21111-4002222-1-1-1-100000000000000000000000000000000000
χ4244444-2-2-4-44-2-24-24-2-2-2-2-21-2-2-211-21-2-22-4222-4111122-1-122-1-1-1-100000−2i32i3i3i3−i3−i300000000000000000000000000000000000
χ4344444-2-2-4-44-2-24-24-2-2-2-2-21-2-2-211-21-2-22-4222-4111122-1-122-1-1-1-1000002i3−2i3−i3−i3i3i300000000000000000000000000000000000
χ444444-244-4-4-244-24-2444-2-24-2-2-244-24-2-2-42-4-4-42-2-2-2-222-4-42222220000000000000000000000000000000000000000000000
χ454444-24-244-244-24-2-2-2-2-21-2-211-2-2-2-2-214-2-2-24-21111-2-2-2-2111111040000000000000-2-2-2-2000011110000000000000000000
χ464444-24-244-244-24-2-2-2-2-21-2-211-2-2-2-2-214-2-2-24-21111-2-2-2-21111110-4000000000000022220000-1-1-1-10000000000000000000
χ474444-24-2-4-4-244-24-2-2-2-2-21-2-211-2-2-2-2-21-4222-4211112222-1-1-1-1-1-100000000000000000−2i32i30000i3i3−i3−i30000000000000000000
χ484444-24-2-4-4-244-24-2-2-2-2-21-2-211-2-2-2-2-21-4222-4211112222-1-1-1-1-1-1000000000000000002i3−2i30000−i3−i3i3i30000000000000000000
χ494444-2-2444-2-2-2-2-2-24441-2-21-2-2-2-21-21-2-2-244-2-2111111-2-2-2-2111100400000000-2-2-2-20000111100000000000000000000000
χ504444-2-2444-2-2-2-2-2-24441-2-21-2-2-2-21-21-2-2-244-2-2111111-2-2-2-2111100-40000000022220000-1-1-1-100000000000000000000000
χ514444-2-24-4-4-2-2-2-2-2-24441-2-21-2-2-2-21-21-222-4-4221111-1-12222-1-1-1-100000000000000000003-3-3300000000000000000000000
χ524444-2-24-4-4-2-2-2-2-2-24441-2-21-2-2-2-21-21-222-4-4221111-1-12222-1-1-1-10000000000000000000-333-300000000000000000000000
χ5344-4-444-24-4-4-44-4-44-2224-2-2-422224-2-4-24-4-22-44-222-24-4-22-22-2-2220000000000000000000000000000000000000000000000
χ5444-4-444-2-44-4-44-4-44-2224-2-2-422224-2-4-2-442-24-4-222-2-442-22-222-2-20000000000000000000000000000000000000000000000
χ5544-4-44-24-44-42-2-4244-4-4-24-22-4-422-2-22424-44-2-4-222-22-22-2-4422-2-20000000000000000000000000000000000000000000000
χ5644-4-44-2-24-4-42-2-424-222-2-21222-1-1-212-2-2-4-22241-1-11-221-1-2211-1-1000−2i32i300i3−i3i3−i300000000000000000000000000000000000
χ5744-4-44-2-24-4-42-2-424-222-2-21222-1-1-212-2-2-4-22241-1-11-221-1-2211-1-10002i3−2i300−i3i3−i3i300000000000000000000000000000000000
χ5844-4-44-2-2-44-42-2-424-222-2-21222-1-1-212-2242-2-2-41-1-112-2-112-2-1-11100000003-3-3300000000000000000000000000000000000
χ5944-4-44-2-2-44-42-2-424-222-2-21222-1-1-212-2242-2-2-41-1-112-2-112-2-1-1110000000-333-300000000000000000000000000000000000
χ6044-4-4-2444-42-442-4-24-4-4-2-24222-4-4-242-2424-4-4-2-222-2-224-4-22-2-2220000000000000000000000000000000000000000000000
χ6144-4-4-24-24-42-442-4-2-222-21-22-1-122-2-22142-22-4-21-1-11-22-221-111-1-1000000000000000000000003-3-330000000000000000000
χ6244-4-4-24-24-42-442-4-2-222-21-22-1-122-2-22142-22-4-21-1-11-22-221-111-1-100000000000000000000000-333-30000000000000000000
χ6344-4-4-24-2-442-442-4-2-222-21-22-1-122-2-221-4-22-2421-1-112-22-2-11-1-111000000000000000−2i32i3000000i3−i3i3−i30000000000000000000
χ6444-4-4-24-2-442-442-4-2-222-21-22-1-122-2-221-4-22-2421-1-112-22-2-11-1-1110000000000000002i3−2i3000000−i3i3−i3i30000000000000000000
χ6544-4-4-2-244-422-222-24-4-41-2-2-122221-2-1-2-224-42-21-1-111-1-22-2211-1-1000000000000023−230000−3−33300000000000000000000000
χ6644-4-4-2-244-422-222-24-4-41-2-2-122221-2-1-2-224-42-21-1-111-1-22-2211-1-10000000000000−2323000033−3−300000000000000000000000
χ6744-4-4-2-24-4422-222-24-4-41-2-2-122221-2-1-22-2-44-221-1-11-112-22-2-1-1110000000000023−23000000−33−3300000000000000000000000
χ6844-4-4-2-24-4422-222-24-4-41-2-2-122221-2-1-22-2-44-221-1-11-112-22-2-1-11100000000000−23230000003−33−300000000000000000000000
χ694-44-44440044-4-4-4-4-44-444444-44-4-4-4-4-400000044-4-400000000000000000000000000000000000000000000000000000000
χ704-44-444-20044-4-4-4-42-224-2-24-22-22-42-42000000-2-22200000000000000000000000000000000000000000000023−23000000000
χ714-44-444-20044-4-4-4-42-224-2-24-22-22-42-42000000-2-222000000000000000000000000000000000000000000000−2323000000000
χ724-44-44-24004-22-42-4-44-4-24-2-24-4-22222-4000000-2-222000000000000000000000000000000000000000000000006−66−600000
χ734-44-44-24004-22-42-4-44-4-24-2-24-4-22222-4000000-2-22200000000000000000000000000000000000000000000000−66−6600000
χ744-44-4-24400-24-42-42-44-4-2-24-2-224-42-422000000-2-222000000000000000000000000000000000000000000000000000i6−i6i6−i60
χ754-44-4-24400-24-42-42-44-4-2-24-2-224-42-422000000-2-222000000000000000000000000000000000000000000000000000−i6i6−i6i60
χ764-4-4444400-4-4-444-4-4-44444-4-44-44-4-44-40000004-44-400000000000000000000000000000000000000000000000000000000
χ774-4-4444-200-4-4-444-422-24-2-2-42-22-2-4242000000-22-22000000000000000000000000000000000000000000023−2300000000000
χ784-4-4444-200-4-4-444-422-24-2-2-42-22-2-4242000000-22-220000000000000000000000000000000000000000000−232300000000000
χ794-4-444-2400-4224-2-4-4-44-24-22-442-222-2-4000000-22-2200000000000000000000000000000000000000000000000i6−i6−i6i600000
χ804-4-444-2400-4224-2-4-4-44-24-22-442-222-2-4000000-22-2200000000000000000000000000000000000000000000000−i6i6i6−i600000
χ814-4-44-244002-4-4-242-4-44-2-2422-2-442-4-22000000-22-220000000000000000000000000000000000000000000000000006−6−660
χ824-4-44-244002-4-4-242-4-44-2-2422-2-442-4-22000000-22-22000000000000000000000000000000000000000000000000000−666−60
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
χ8588-8-8-4-4-48-844-444-4-444222-2-2-2-2-222-22-44-444-4-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000
χ8688-8-8-4-4-4-8844-444-4-444222-2-2-2-2-222-224-44-4-44-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000
χ878-88-88-4-4008-44-84-84-44-4-42-4-442-24-24400000022-2-200000000000000000000000000000000000000000000000000000000
χ888-88-8-48-400-48-84-844-44-42-4-42-2-44444-200000022-2-200000000000000000000000000000000000000000000000000000000
χ898-88-8-4-4800-4-44444-88-82-4-42-44-44-24-2400000022-2-200000000000000000000000000000000000000000000000000000000
χ908-88-8-4-4-400-4-444444-4422222-22-2-2-2-2-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000
χ918-88-8-4-4-400-4-444444-4422222-22-2-2-2-2-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000
χ928-8-888-4-400-8448-4-844-4-4-4244-4-224-2-440000002-22-200000000000000000000000000000000000000000000000000000000
χ938-8-88-48-4004-8-8-48444-4-42-44-224-444-4-20000002-22-200000000000000000000000000000000000000000000000000000000
χ948-8-88-4-4800444-4-44-8-882-4-4-24-44-4-24240000002-22-200000000000000000000000000000000000000000000000000000000
χ958-8-88-4-4-400444-4-4444-4222-2-22-22-2-22-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000
χ968-8-88-4-4-400444-4-4444-4222-2-22-22-2-22-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000

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