Finite Group Databasebeta

← Group #13156561

Character table — Group #13156561

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222244444444444444444488888888888888242424242424242424242424242424242424242424242424242424363636363636363636363636363636363636216
order122233344666666666333666666666121212121212366612121212121212121212224666666666666666612121212121212124488881212121224242424242424244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1111-1-111-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111
χ511111111111111111111111111111111111111111111111111-111-1-111-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1
χ611111111111111111111111111111111111111111111111111-11-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11
χ711111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11
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
χ11222222-1222222-122-1-12-1-12-1-1-1-12-1-1222-1-122-1-1-1-122-1-1-1-1-1-1-1-12202222-1-1-1-1-1-1-1-1-1-1-1-100000000220000-1-1-1-1000000000
χ12222222-1222222-122-1-12-1-12-1-1-1-12-1-1222-1-122-1-1-1-122-1-1-1-1-1-1-1-12-2022-2-2-1-111-1-1-1-1111100000000-2-200001111000000000
χ13222222-1222222-122-1-12-1-12-1-1-1-12-1-1222-1-122-1-1-1-122-1-1-1-1-1-1-1-1-220-2-22211-1-11111-1-1-1-100000000-2-200001111000000000
χ14222222-1222222-122-1-12-1-12-1-1-1-12-1-1222-1-122-1-1-1-122-1-1-1-1-1-1-1-1-2-20-2-2-2-211111111111100000000220000-1-1-1-1000000000
χ15222222-1-2-22222-122-1-12-1-12-1-1-1-12-1-12-2-211-2-2-1-1-1-1-2-2111111110000000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i3000000002-20000-1-111000000000
χ16222222-1-2-22222-122-1-12-1-12-1-1-1-12-1-12-2-211-2-2-1-1-1-1-2-2111111110000000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i300000000-22000011-1-1000000000
χ17222222-1-2-22222-122-1-12-1-12-1-1-1-12-1-12-2-211-2-2-1-1-1-1-2-2111111110000000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i300000000-22000011-1-1000000000
χ18222222-1-2-22222-122-1-12-1-12-1-1-1-12-1-12-2-211-2-2-1-1-1-1-2-2111111110000000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3000000002-20000-1-111000000000
χ1922222-12222-12-122-122-12-1-122-1-1-12-1-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-102200-1-100220000-1-1-1-122-1-1-1-1-1-100002200000000-1-1-1-10
χ2022222-12222-12-122-122-12-1-122-1-1-12-1-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-102-200-1-100220000-1-1-1-1-2-21111110000-2-20000000011110
χ2122222-12222-12-122-122-12-1-122-1-1-12-1-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-10-22001100-2-20000111122-1-1-1-1-1-10000-2-20000000011110
χ2222222-12222-12-122-122-12-1-122-1-1-12-1-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-10-2-2001100-2-200001111-2-211111100002200000000-1-1-1-10
χ232222-12222-12-122-1222-1-12-1-1-122-1-12-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-1202-1-1002200-1-1-1-10000-1-122-1-1-1-10022000000-1-1-1-100000
χ242222-12222-12-122-1222-1-12-1-1-122-1-12-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-120-2-1-1002200-1-1-1-1000011-2-2111100-2-2000000111100000
χ252222-12222-12-122-1222-1-12-1-1-122-1-12-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2021100-2-20011110000-1-122-1-1-1-100-2-2000000111100000
χ262222-12222-12-122-1222-1-12-1-1-122-1-12-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-20-21100-2-2001111000011-2-211110022000000-1-1-1-100000
χ2722-2-22222-2-2-2222-2-2-2-2222-2-2-2-2-2222-22-22-2-222-2-222-22-22-222-2-2000000000000000000000000000002i−2i0000002i2i−2i−2i00000
χ2822-2-22222-2-2-2222-2-2-2-2222-2-2-2-2-2222-22-22-2-222-2-222-22-22-222-2-200000000000000000000000000000−2i2i000000−2i−2i2i2i00000
χ2922-2-2222-22-2-2222-2-2-2-2222-2-2-2-2-2222-2-22-222-22-2-22-22-22-22-2-22200000000000000000000000000000002i−2i000000002i2i−2i−2i0
χ3022-2-2222-22-2-2222-2-2-2-2222-2-2-2-2-2222-2-22-222-22-2-22-22-22-22-2-2220000000000000000000000000000000−2i2i00000000−2i−2i2i2i0
χ3122-2-22-12-22-212-12-21-2-2-12-11-2-211-12-11-2-1-2221-111-11-1-221-111-1-100000−i3i300000000−i3i3−i3i3003−333−3−300002i−2i00000000−i−iii0
χ3222-2-22-12-22-212-12-21-2-2-12-11-2-211-12-11-2-1-2221-111-11-1-221-111-1-100000−i3i300000000−i3i3−i3i300−33−3−3330000−2i2i00000000ii−i−i0
χ3322-2-22-12-22-212-12-21-2-2-12-11-2-211-12-11-2-1-2221-111-11-1-221-111-1-100000i3−i300000000i3−i3i3−i3003−333−3−30000−2i2i00000000ii−i−i0
χ3422-2-22-12-22-212-12-21-2-2-12-11-2-211-12-11-2-1-2221-111-11-1-221-111-1-100000i3−i300000000i3−i3i3−i300−33−3−33300002i−2i00000000−i−iii0
χ3522-2-2-1222-21-2-1221-2-2-2-1-12111-2-2-1-121-1-22-212-111-1-11-112-2-1-111000−i3i3000000−i3i3−i3i300003−3003−33−3002i−2i000000−i−iii00000
χ3622-2-2-1222-21-2-1221-2-2-2-1-12111-2-2-1-121-1-22-212-111-1-11-112-2-1-111000−i3i3000000−i3i3−i3i30000−3300−33−3300−2i2i000000ii−i−i00000
χ3722-2-2-1222-21-2-1221-2-2-2-1-12111-2-2-1-121-1-22-212-111-1-11-112-2-1-111000i3−i3000000i3−i3i3−i300003−3003−33−300−2i2i000000ii−i−i00000
χ3822-2-2-1222-21-2-1221-2-2-2-1-12111-2-2-1-121-1-22-212-111-1-11-112-2-1-111000i3−i3000000i3−i3i3−i30000−3300−33−33002i−2i000000−i−iii00000
χ3944444-24-4-44-24-244-244-24-2-244-2-2-24-2-2-42-4-4-42-2-2-2-222-4-42222220000000000000000000000000000000000000000000000
χ4044444-2-2444-24-2-24-2-2-2-2-21-2-2-211-2-21-24-2-2-24-21111-2-2-2-211111104000-2-200-2-200001111000000000000000000000000000
χ4144444-2-2444-24-2-24-2-2-2-2-21-2-2-211-2-21-24-2-2-24-21111-2-2-2-21111110-40002200220000-1-1-1-1000000000000000000000000000
χ4244444-2-2-4-44-24-2-24-2-2-2-2-21-2-2-211-2-21-2-4222-4211112222-1-1-1-1-1-1000000000−2i32i30000i3i3−i3−i3000000000000000000000000000
χ4344444-2-2-4-44-24-2-24-2-2-2-2-21-2-2-211-2-21-2-4222-4211112222-1-1-1-1-1-10000000002i3−2i30000−i3−i3i3i3000000000000000000000000000
χ444444-244-4-4-24-244-2444-2-24-2-2-244-2-24-22-4-4-42-4-2-2-2-22222-4-422220000000000000000000000000000000000000000000000
χ454444-24-244-24-24-2-24-2-2-21-2-211-2-2-21-2-2-24-2-2-241111-2-211-2-21111400-2-200-2-20011110000000000000000000000000000000
χ464444-24-244-24-24-2-24-2-2-21-2-211-2-2-21-2-2-24-2-2-241111-2-211-2-21111-40022002200-1-1-1-10000000000000000000000000000000
χ474444-24-2-4-4-24-24-2-24-2-2-21-2-211-2-2-21-2-22-4222-4111122-1-122-1-1-1-10000000−2i32i300i3i3−i3−i30000000000000000000000000000000
χ484444-24-2-4-4-24-24-2-24-2-2-21-2-211-2-2-21-2-22-4222-4111122-1-122-1-1-1-100000002i3−2i300−i3−i3i3i30000000000000000000000000000000
χ494444-2-2444-2-2-2-24-2-2441-2-21-2-2-2-21-2-21-2-244-2-2111111-2-2-2-211110040000000000000000-2-2-2-211110000000000000000000
χ504444-2-2444-2-2-2-24-2-2441-2-21-2-2-2-21-2-21-2-244-2-2111111-2-2-2-2111100-400000000000000002222-1-1-1-10000000000000000000
χ514444-2-24-4-4-2-2-2-24-2-2441-2-21-2-2-2-21-2-2122-4-4221111-1-12222-1-1-1-1000000000000000000000003-3-330000000000000000000
χ524444-2-24-4-4-2-2-2-24-2-2441-2-21-2-2-2-21-2-2122-4-4221111-1-12222-1-1-1-100000000000000000000000-333-30000000000000000000
χ5344-4-444-24-4-4-444-2-4-4224-2-2-422224-2-2-44-4-22-44-222-24-4-22-22-2-2220000000000000000000000000000000000000000000000
χ5444-4-444-2-44-4-444-2-4-4224-2-2-422224-2-2-4-442-24-4-222-2-442-22-222-2-20000000000000000000000000000000000000000000000
χ5544-4-44-244-4-424-24-42-4-4-24-22-4-422-24-22424-4-4-2-222-2-224-4-22-2-2220000000000000000000000000000000000000000000000
χ5644-4-44-2-24-4-424-2-2-4222-2-21222-1-1-2-21242-22-4-21-1-11-22-221-111-1-10000000000000003-3-33000000000000000000000000000
χ5744-4-44-2-24-4-424-2-2-4222-2-21222-1-1-2-21242-22-4-21-1-11-22-221-111-1-1000000000000000-333-3000000000000000000000000000
χ5844-4-44-2-2-44-424-2-2-4222-2-21222-1-1-2-212-4-22-2421-1-112-22-2-11-1-11100000−2i32i300000000i3−i3i3−i3000000000000000000000000000
χ5944-4-44-2-2-44-424-2-2-4222-2-21222-1-1-2-212-4-22-2421-1-112-22-2-11-1-111000002i3−2i300000000−i3i3−i3i3000000000000000000000000000
χ6044-4-4-244-442-4-2442-4-4-4-2-24222-4-4-2-24224-44-2-4-222-22-22-2-4422-2-20000000000000000000000000000000000000000000000
χ6144-4-4-24-24-42-4-24-22-422-21-22-1-122-21-22-2-4-22241-1-11-221-1-2211-1-1000−2i32i3000000i3−i3i3−i30000000000000000000000000000000
χ6244-4-4-24-24-42-4-24-22-422-21-22-1-122-21-22-2-4-22241-1-11-221-1-2211-1-10002i3−2i3000000−i3i3−i3i30000000000000000000000000000000
χ6344-4-4-24-2-442-4-24-22-422-21-22-1-122-21-22242-2-2-41-1-112-2-112-2-1-111000000000003-3-330000000000000000000000000000000
χ6444-4-4-24-2-442-4-24-22-422-21-22-1-122-21-22242-2-2-41-1-112-2-112-2-1-11100000000000-333-30000000000000000000000000000000
χ6544-4-4-2-244-422-2-2422-4-41-2-2-122221-2-2-1-224-42-21-1-111-1-22-2211-1-1000000000000000000023−2300−33−330000000000000000000
χ6644-4-4-2-244-422-2-2422-4-41-2-2-122221-2-2-1-224-42-21-1-111-1-22-2211-1-10000000000000000000−2323003−33−30000000000000000000
χ6744-4-4-2-24-4422-2-2422-4-41-2-2-122221-2-2-12-2-44-221-1-11-112-22-2-1-11100000000000000000000023−23−3−3330000000000000000000
χ6844-4-4-2-24-4422-2-2422-4-41-2-2-122221-2-2-12-2-44-221-1-11-112-22-2-1-111000000000000000000000−232333−3−30000000000000000000
χ694-44-444400-4-4-4-4-4444-4444-44-44-4-4-4-4400000044-4-400000000000000000000000000000000000000000000000000000000
χ704-44-444-200-4-4-4-4244-224-2-2-4-22-22-4224000000-2-2220000000000000000000000000000000000000000000−2i32i300000000000
χ714-44-444-200-4-4-4-4244-224-2-2-4-22-22-4224000000-2-22200000000000000000000000000000000000000000002i3−2i300000000000
χ724-44-44-2400-42-42-44-24-4-24-224-4-222-42-2000000-2-222000000000000000000000000000000000000000000000000000i6−i6i6−i60
χ734-44-44-2400-42-42-44-24-4-24-224-4-222-42-2000000-2-222000000000000000000000000000000000000000000000000000−i6i6−i6i60
χ744-44-4-244002-42-4-4-244-4-2-242-224-422-4-2000000-2-22200000000000000000000000000000000000000000000000i6−i6i6−i600000
χ754-44-4-244002-42-4-4-244-4-2-242-224-422-4-2000000-2-22200000000000000000000000000000000000000000000000−i6i6−i6i600000
χ764-4-444440044-4-4-4-4-4-444444-44-44-4-4-4-40000004-44-400000000000000000000000000000000000000000000000000000000
χ774-4-4444-20044-4-42-4-42-24-2-242-22-2-422-4000000-22-22000000000000000000000000000000000000000000000−2i32i3000000000
χ784-4-4444-20044-4-42-4-42-24-2-242-22-2-422-4000000-22-220000000000000000000000000000000000000000000002i3−2i3000000000
χ794-4-444-24004-2-42-4-42-44-24-2-2-442-22-422000000-22-220000000000000000000000000000000000000000000000000006−6−660
χ804-4-444-24004-2-42-4-42-44-24-2-2-442-22-422000000-22-22000000000000000000000000000000000000000000000000000−666−60
χ814-4-44-24400-242-4-42-4-44-2-24-22-2-4422-42000000-22-22000000000000000000000000000000000000000000000006−6−6600000
χ824-4-44-24400-242-4-42-4-44-2-24-22-2-4422-42000000-22-2200000000000000000000000000000000000000000000000−666−600000
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
χ8588-8-8-4-4-48-844-4-4-44444222-2-2-2-2-2222-2-44-444-4-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000
χ8688-8-8-4-4-4-8844-4-4-44444222-2-2-2-2-2222-24-44-4-44-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000
χ878-88-88-4-400-84-8448-4-44-4-424-442-244-2-400000022-2-200000000000000000000000000000000000000000000000000000000
χ888-88-8-48-4004-84-84-48-44-42-442-2-444-24-400000022-2-200000000000000000000000000000000000000000000000000000000
χ898-88-8-4-48004444-8-4-48-82-4-4-2-44-44-244200000022-2-200000000000000000000000000000000000000000000000000000000
χ908-88-8-4-4-40044444-4-4-44222-22-22-2-2-2-22000000-1-11100000033−3333−330000000000000000000000000000000000000000000000
χ918-88-8-4-4-40044444-4-4-44222-22-22-2-2-2-22000000-1-111000000−3333−33330000000000000000000000000000000000000000000000
χ928-8-888-4-4008-4-844-844-4-4-42-44-4-2244-240000002-22-200000000000000000000000000000000000000000000000000000000
χ938-8-88-48-400-484-844-84-4-42-4-4-224-44-2440000002-22-200000000000000000000000000000000000000000000000000000000
χ948-8-88-4-4800-4-444-844-882-4-424-44-4-244-20000002-22-200000000000000000000000000000000000000000000000000000000
χ958-8-88-4-4-400-4-4444444-42222-22-22-2-2-2-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000
χ968-8-88-4-4-400-4-4444444-42222-22-22-2-2-2-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000

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