Finite Group Databasebeta

← Group #13155977

Character table — Group #13155977

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size111122222222222222444444444444444444888888888888881212181824242424242424242424242424242424242424242424242424243636363636363636363636363636363636108108
order122233344666666666333666666666121212121212366612121212121212121212444422666666666666666612121212121212124888812121212242424242424242422
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111111111111-1-11-111-1-111-1-11111-1-1-1-111111111-111-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-11-1-111-1-111-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ511111111111111111111111111111111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1
χ711111111111111111111111111111111111111111111111111-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ92222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2002200000000000000000000000000-2000022-2-20000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-200-2-20000000000000000000000000020000-2-2220000000000
χ11222222-1222222-122-1-12-1-12-1-1-1-12-1-1222-1-122-1-1-1-122-1-1-1-1-1-1-1-10022222222-1-1-1-1-1-1-1-1-1-1-1-10000000020000-1-1-1-10000000000
χ12222222-1222222-122-1-12-1-12-1-1-1-12-1-1222-1-122-1-1-1-122-1-1-1-1-1-1-1-10022-2-2-2-2-2-21111111111110000000020000-1-1-1-10000000000
χ13222222-1222222-122-1-12-1-12-1-1-1-12-1-1222-1-122-1-1-1-122-1-1-1-1-1-1-1-100-2-22-222-2-2-1-111-1-1-1-1111100000000-2000011110000000000
χ14222222-1222222-122-1-12-1-12-1-1-1-12-1-1222-1-122-1-1-1-122-1-1-1-1-1-1-1-100-2-2-22-2-22211-1-11111-1-1-1-100000000-2000011110000000000
χ15222222-1-2-22222-122-1-12-1-12-1-1-1-12-1-12-2-211-2-2-1-1-1-1-2-2111111110022000000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i300000000-20000-1-1110000000000
χ16222222-1-2-22222-122-1-12-1-12-1-1-1-12-1-12-2-211-2-2-1-1-1-1-2-2111111110022000000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i300000000-20000-1-1110000000000
χ17222222-1-2-22222-122-1-12-1-12-1-1-1-12-1-12-2-211-2-2-1-1-1-1-2-21111111100-2-2000000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i3000000002000011-1-10000000000
χ18222222-1-2-22222-122-1-12-1-12-1-1-1-12-1-12-2-211-2-2-1-1-1-1-2-21111111100-2-2000000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i3000000002000011-1-10000000000
χ1922222-12222-12-122-122-12-1-122-1-1-12-1-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-122000200-1-100220000-1-1-1-122-1-1-1-1-1-10002200000000-1-1-1-100
χ2022222-12222-12-122-122-12-1-122-1-1-12-1-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-122000-2001100-2-20000111122-1-1-1-1-1-1000-2-200000000111100
χ2122222-12222-12-122-122-12-1-122-1-1-12-1-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2000200-1-100220000-1-1-1-1-2-2111111000-2-200000000111100
χ2222222-12222-12-122-122-12-1-122-1-1-12-1-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2000-2001100-2-200001111-2-21111110002200000000-1-1-1-100
χ232222-12222-12-122-1222-1-12-1-1-122-1-12-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-1220020-1-1002200-1-1-1-10000-1-122-1-1-1-1022000000-1-1-1-1000000
χ242222-12222-12-122-1222-1-12-1-1-122-1-12-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-12200-201100-2-20011110000-1-122-1-1-1-10-2-20000001111000000
χ252222-12222-12-122-1222-1-12-1-1-122-1-12-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-20020-1-1002200-1-1-1-1000011-2-211110-2-20000001111000000
χ262222-12222-12-122-1222-1-12-1-1-122-1-12-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-200-201100-2-2001111000011-2-21111022000000-1-1-1-1000000
χ2722-2-22222-2-2-2222-2-2-2-2222-2-2-2-2-2222-2222-2-2-22-2-222-22-22-222-2-22i−2i000000000000000000002i−2i2i−2i2i2i−2i−2i0000000000000000000
χ2822-2-22222-2-2-2222-2-2-2-2222-2-2-2-2-2222-2222-2-2-22-2-222-22-22-222-2-2−2i2i00000000000000000000−2i2i−2i2i−2i−2i2i2i0000000000000000000
χ2922-2-2222-22-2-2222-2-2-2-2222-2-2-2-2-2222-2-2-2-22222-2-22-22-22-22-2-222000000000000000000000000000000000000000000000002-2
χ3022-2-2222-22-2-2222-2-2-2-2222-2-2-2-2-2222-2-2-2-22222-2-22-22-22-22-2-22200000000000000000000000000000000000000000000000-22
χ3122-2-22-122-2-212-12-21-2-2-12-11-2-211-12-112-12-2-21-111-1-112-2-11-1-1112i−2i000000−i3i300000000−i3i3−i3i32i−2i−ii−i−iii000000000000033−3−300
χ3222-2-22-122-2-212-12-21-2-2-12-11-2-211-12-112-12-2-21-111-1-112-2-11-1-1112i−2i000000i3−i300000000i3−i3i3−i32i−2i−ii−i−iii0000000000000−3−33300
χ3322-2-22-122-2-212-12-21-2-2-12-11-2-211-12-112-12-2-21-111-1-112-2-11-1-111−2i2i000000−i3i300000000−i3i3−i3i3−2i2ii−iii−i−i0000000000000−3−33300
χ3422-2-22-122-2-212-12-21-2-2-12-11-2-211-12-112-12-2-21-111-1-112-2-11-1-111−2i2i000000i3−i300000000i3−i3i3−i3−2i2ii−iii−i−i000000000000033−3−300
χ3522-2-2-1222-21-2-1221-2-2-2-1-12111-2-2-1-121-122-21-2-111-1-11-112-2-1-1112i−2i0000−i3i3000000−i3i3−i3i30000−ii2i−2i−i−iii00000000033−3−3000000
χ3622-2-2-1222-21-2-1221-2-2-2-1-12111-2-2-1-121-122-21-2-111-1-11-112-2-1-1112i−2i0000i3−i3000000i3−i3i3−i30000−ii2i−2i−i−iii000000000−3−333000000
χ3722-2-2-1222-21-2-1221-2-2-2-1-12111-2-2-1-121-122-21-2-111-1-11-112-2-1-111−2i2i0000−i3i3000000−i3i3−i3i30000i−i−2i2iii−i−i000000000−3−333000000
χ3822-2-2-1222-21-2-1221-2-2-2-1-12111-2-2-1-121-122-21-2-111-1-11-112-2-1-111−2i2i0000i3−i3000000i3−i3i3−i30000i−i−2i2iii−i−i00000000033−3−3000000
χ392-2-2222200-2-2-2-2-2222-2222-22-22-2-2-2-2200000022-2-20000000000002-20000000000000000000000000002−22−22-2002−22−22−22−200
χ402-2-2222200-2-2-2-2-2222-2222-22-22-2-2-2-2200000022-2-20000000000002-2000000000000000000000000000−22−222-200−22−22−22−2200
χ412-2-2222200-2-2-2-2-2222-2222-22-22-2-2-2-2200000022-2-2000000000000-220000000000000000000000000002−2−22-22002−22−2−22−2200
χ422-2-2222200-2-2-2-2-2222-2222-22-22-2-2-2-2200000022-2-2000000000000-22000000000000000000000000000−222−2-2200−22−222−22−200
χ4344444-24-4-44-24-244-244-24-2-244-2-2-24-2-2-42-4-4-42-2-2-2-222-4-42222220000000000000000000000000000000000000000000000000
χ4444444-2-2444-24-2-24-2-2-2-2-21-2-2-211-2-21-24-2-2-24-21111-2-2-2-211111100000400-2-200-2-200001111000000000000000000000000000
χ4544444-2-2444-24-2-24-2-2-2-2-21-2-2-211-2-21-24-2-2-24-21111-2-2-2-211111100000-4002200220000-1-1-1-1000000000000000000000000000
χ4644444-2-2-4-44-24-2-24-2-2-2-2-21-2-2-211-2-21-2-4222-4211112222-1-1-1-1-1-1000000000000−2i32i30000i3i3−i3−i3000000000000000000000000000
χ4744444-2-2-4-44-24-2-24-2-2-2-2-21-2-2-211-2-21-2-4222-4211112222-1-1-1-1-1-10000000000002i3−2i30000−i3−i3i3i3000000000000000000000000000
χ484444-244-4-4-24-244-2444-2-24-2-2-244-2-24-22-4-4-42-4-2-2-2-22222-4-422220000000000000000000000000000000000000000000000000
χ494444-24-244-24-24-2-24-2-2-21-2-211-2-2-21-2-2-24-2-2-241111-2-211-2-21111000040-2-200-2-20011110000000000000000000000000000000
χ504444-24-244-24-24-2-24-2-2-21-2-211-2-2-21-2-2-24-2-2-241111-2-211-2-211110000-4022002200-1-1-1-10000000000000000000000000000000
χ514444-24-2-4-4-24-24-2-24-2-2-21-2-211-2-2-21-2-22-4222-4111122-1-122-1-1-1-10000000000−2i32i300i3i3−i3−i30000000000000000000000000000000
χ524444-24-2-4-4-24-24-2-24-2-2-21-2-211-2-2-21-2-22-4222-4111122-1-122-1-1-1-100000000002i3−2i300−i3−i3i3i30000000000000000000000000000000
χ534444-2-2444-2-2-2-24-2-2441-2-21-2-2-2-21-2-21-2-244-2-2111111-2-2-2-211114400000000000000000000-2-2-2-211110000000000000000000
χ544444-2-2444-2-2-2-24-2-2441-2-21-2-2-2-21-2-21-2-244-2-2111111-2-2-2-21111-4-4000000000000000000002222-1-1-1-10000000000000000000
χ554444-2-24-4-4-2-2-2-24-2-2441-2-21-2-2-2-21-2-2122-4-4221111-1-12222-1-1-1-1000000000000000000000000003-33-30000000000000000000
χ564444-2-24-4-4-2-2-2-24-2-2441-2-21-2-2-2-21-2-2122-4-4221111-1-12222-1-1-1-100000000000000000000000000-33-330000000000000000000
χ5744-4-444-24-4-4-444-2-4-4224-2-2-422224-2-2-444-22-4-4-222-24-4-22-22-2-2220000000000000000000000000000000000000000000000000
χ5844-4-444-2-44-4-444-2-4-4224-2-2-422224-2-2-4-4-42-244-222-2-442-22-222-2-20000000000000000000000000000000000000000000000000
χ5944-4-44-24-44-424-24-42-4-4-24-22-4-422-24-22-42-444-2-222-22-2-442-222-2-20000000000000000000000000000000000000000000000000
χ6044-4-44-2-24-4-424-2-2-4222-2-21222-1-1-2-2124-2-22-421-1-11-22-221-111-1-100000000−2i32i300000000i3−i3i3−i3000000000000000000000000000
χ6144-4-44-2-24-4-424-2-2-4222-2-21222-1-1-2-2124-2-22-421-1-11-22-221-111-1-1000000002i3−2i300000000−i3i3−i3i3000000000000000000000000000
χ6244-4-44-2-2-44-424-2-2-4222-2-21222-1-1-2-212-422-24-21-1-112-22-2-11-1-1110000000000000000003-3-33000000000000000000000000000
χ6344-4-44-2-2-44-424-2-2-4222-2-21222-1-1-2-212-422-24-21-1-112-22-2-11-1-111000000000000000000-333-3000000000000000000000000000
χ6444-4-4-244-442-4-2442-4-4-4-2-24222-4-4-2-2422-4-44-24-222-22-22-2-4422-2-20000000000000000000000000000000000000000000000000
χ6544-4-4-24-24-42-4-24-22-422-21-22-1-122-21-22-24-222-41-1-11-221-1-2211-1-1000000−2i32i3000000i3−i3i3−i30000000000000000000000000000000
χ6644-4-4-24-24-42-4-24-22-422-21-22-1-122-21-22-24-222-41-1-11-221-1-2211-1-10000002i3−2i3000000−i3i3−i3i30000000000000000000000000000000
χ6744-4-4-24-2-442-4-24-22-422-21-22-1-122-21-222-42-2-241-1-112-2-112-2-1-111000000000000003-3-330000000000000000000000000000000
χ6844-4-4-24-2-442-4-24-22-422-21-22-1-122-21-222-42-2-241-1-112-2-112-2-1-11100000000000000-333-30000000000000000000000000000000
χ6944-4-4-2-244-422-2-2422-4-41-2-2-122221-2-2-1-2-24-4221-1-111-1-22-2211-1-14i−4i00000000000000000000−2i2i−2i2iii−i−i0000000000000000000
χ7044-4-4-2-244-422-2-2422-4-41-2-2-122221-2-2-1-2-24-4221-1-111-1-22-2211-1-1−4i4i000000000000000000002i−2i2i−2i−i−iii0000000000000000000
χ7144-4-4-2-24-4422-2-2422-4-41-2-2-122221-2-2-122-44-2-21-1-11-112-22-2-1-111000000000000000000000000003i−3i−3i3i0000000000000000000
χ7244-4-4-2-24-4422-2-2422-4-41-2-2-122221-2-2-122-44-2-21-1-11-112-22-2-1-11100000000000000000000000000−3i3i3i−3i0000000000000000000
χ734-44-44440044-4-4-4-4-4-444444-44-44-4-4-4-40000004-44-400000000000000000000000000000000000000000000000000000000000
χ744-44-444-20044-4-42-4-42-24-2-242-22-2-422-4000000-22-2200000000000000000000000000000000000000000000000−2i32i30000000000
χ754-44-444-20044-4-42-4-42-24-2-242-22-2-422-4000000-22-22000000000000000000000000000000000000000000000002i3−2i30000000000
χ764-44-44-24004-2-42-4-42-44-24-2-2-442-22-422000000-22-22000000000000000000000000000000000000000000000000000006−6−6600
χ774-44-44-24004-2-42-4-42-44-24-2-2-442-22-422000000-22-2200000000000000000000000000000000000000000000000000000−666−600
χ784-44-4-24400-242-4-42-4-44-2-24-22-2-4422-42000000-22-2200000000000000000000000000000000000000000000000006−6−66000000
χ794-44-4-24400-242-4-42-4-44-2-24-22-2-4422-42000000-22-220000000000000000000000000000000000000000000000000−666−6000000
χ804-4-4444-200-4-4-4-4244-224-2-2-4-22-22-4224000000-2-2220000000000004-40000000000000000000000000000000-22000000000000
χ814-4-4444-200-4-4-4-4244-224-2-2-4-22-22-4224000000-2-222000000000000-4400000000000000000000000000000002-2000000000000
χ824-4-444-2400-42-42-44-24-4-24-224-4-222-42-2000000-2-222000000000000000000000000000000000000000000022−2200000000−22−2200
χ834-4-444-2400-42-42-44-24-4-24-224-4-222-42-2000000-2-2220000000000000000000000000000000000000000000−2222000000002−22−200
χ844-4-44-244002-42-4-4-244-4-2-242-224-422-4-2000000-2-2220000000000000000000000000000000000000000022−22000000−22−22000000
χ854-4-44-244002-42-4-4-244-4-2-242-224-422-4-2000000-2-22200000000000000000000000000000000000000000−22220000002−22−2000000
χ868888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000000
χ878888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000000
χ8888-8-8-4-4-48-844-4-4-44444222-2-2-2-2-2222-2-4-4-4444-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000000
χ8988-8-8-4-4-4-8844-4-4-44444222-2-2-2-2-2222-2444-4-4-4-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000000
χ908-88-88-4-4008-4-844-844-4-4-42-44-4-2244-240000002-22-200000000000000000000000000000000000000000000000000000000000
χ918-88-8-48-400-484-844-84-4-42-4-4-224-44-2440000002-22-200000000000000000000000000000000000000000000000000000000000
χ928-88-8-4-4800-4-444-844-882-4-424-44-4-244-20000002-22-200000000000000000000000000000000000000000000000000000000000
χ938-88-8-4-4-400-4-4444444-42222-22-22-2-2-2-2000000-11-1100000033−3333−330000000000000000000000000000000000000000000000000
χ948-88-8-4-4-400-4-4444444-42222-22-22-2-2-2-2000000-11-11000000−3333−33330000000000000000000000000000000000000000000000000
χ958-8-888-4-400-84-8448-4-44-4-424-442-244-2-400000022-2-200000000000000000000000000000000000000000000000000000000000
χ968-8-88-48-4004-84-84-48-44-42-442-2-444-24-400000022-2-200000000000000000000000000000000000000000000000000000000000
χ978-8-88-4-48004444-8-4-48-82-4-4-2-44-44-244200000022-2-200000000000000000000000000000000000000000000000000000000000
χ988-8-88-4-4-40044444-4-4-44222-22-22-2-2-2-22000000-1-11100000033−33−33330000000000000000000000000000000000000000000000000
χ998-8-88-4-4-40044444-4-4-44222-22-22-2-2-2-22000000-1-111000000−333333−330000000000000000000000000000000000000000000000000

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