Finite Group Databasebeta

← Group #13156430

Character table — Group #13156430

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size111122222222222222444444444444444444888888888888881212181824242424242424242424242424242424242424242424242424243636363636363636363636363636363636108108
order122233344666666666333666666666121212121212366612121212121212121212444424666666661212121212121212121212121212121226688881212242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111111111111-1-11-11111111111-1-111-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1
χ511111111111111111111111111111111111111111111111111-1-1111111111111-1-111-1-111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
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
χ711111111111111111111111111111111111111111111111111-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-111-1-1-1-11111-1-1-1-111
χ92222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2002200000000000000000000000000-2-2-20000220000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-200-2-2000000000000000000000000002220000-2-20000000000
χ11222222-12222-1222-1-122-1-12-1-1-12-1-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100222222-1-1-1-1-1-100-1-100220000-1-1-1-12-1-10000-1-10000000000
χ12222222-12222-1222-1-122-1-12-1-1-12-1-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-10022-2-2-2-2111111001100-2-2000011112-1-10000-1-10000000000
χ13222222-12222-1222-1-122-1-12-1-1-12-1-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100-2-22-222-1-1-1-1-1-1001100-2-200001111-2110000110000000000
χ14222222-12222-1222-1-122-1-12-1-1-12-1-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100-2-2-22-2-211111100-1-100220000-1-1-1-1-2110000110000000000
χ15222222-1-2-222-1222-1-122-1-12-1-1-12-1-12-1-2-211-2-2-1-1-1-1-2-21111111100220000−i3i3−i3−i3i3i300−i3i300000000−i3−i3i3i3-2110000-1-10000000000
χ16222222-1-2-222-1222-1-122-1-12-1-1-12-1-12-1-2-211-2-2-1-1-1-1-2-21111111100220000i3−i3i3i3−i3−i300i3−i300000000i3i3−i3−i3-2110000-1-10000000000
χ17222222-1-2-222-1222-1-122-1-12-1-1-12-1-12-1-2-211-2-2-1-1-1-1-2-21111111100-2-20000−i3i3−i3−i3i3i300i3−i300000000i3i3−i3−i32-1-10000110000000000
χ18222222-1-2-222-1222-1-122-1-12-1-1-12-1-12-1-2-211-2-2-1-1-1-1-2-21111111100-2-20000i3−i3i3i3−i3−i300−i3i300000000−i3−i3i3i32-1-10000110000000000
χ1922222-12222-122-1-1222-12-1-12-1-1-12-1-122-1222-1-1-1-1-1-1-122-1-1-1-1-1-1220020-1-122-1-1-1-1-1-1002200-1-1-1-10000000220000-1-1-1-1000000
χ2022222-12222-122-1-1222-12-1-12-1-1-12-1-122-1222-1-1-1-1-1-1-122-1-1-1-1-1-12200-2011-2-21111-1-1002200-1-1-1-10000000-2-200001111000000
χ2122222-12222-122-1-1222-12-1-12-1-1-12-1-122-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-2-20020-1-122-1-1-1-11100-2-20011110000000-2-200001111000000
χ2222222-12222-122-1-1222-12-1-12-1-1-12-1-122-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2011-2-211111100-2-20011110000000220000-1-1-1-1000000
χ232222-12222-122-12222-1-1-12-1-122-1-12-1-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-1220002000000002222-1-1-1-1-1-1-1-1-1-1-1-10000022000000-1-1-1-100
χ242222-12222-122-12222-1-1-12-1-122-1-12-1-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-122000-20000000022-2-2-1-111-1-1-1-1111100000-2-2000000111100
χ252222-12222-122-12222-1-1-12-1-122-1-12-1-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-2000200000000-2-22211-1-11111-1-1-1-100000-2-2000000111100
χ262222-12222-122-12222-1-1-12-1-122-1-12-1-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-1-2-2000-200000000-2-2-2-21111111111110000022000000-1-1-1-100
χ2722-2-22222-2-2-2-222-2-22-2222-2-2-2-2222-2-22-22-2-222-2-222-22-22-222-2-2000000000000000000000000000000000000000000000002i−2i
χ2822-2-22222-2-2-2-222-2-22-2222-2-2-2-2222-2-22-22-2-222-2-222-22-22-222-2-200000000000000000000000000000000000000000000000−2i2i
χ2922-2-2222-22-2-2-222-2-22-2222-2-2-2-2222-2-2-22-222-22-2-22-22-22-22-2-2222i−2i0000000000002i−2i002i−2i002i2i−2i−2i00000000000000000000000
χ3022-2-2222-22-2-2-222-2-22-2222-2-2-2-2222-2-2-22-222-22-2-22-22-22-22-2-222−2i2i000000000000−2i2i00−2i2i00−2i−2i2i2i00000000000000000000000
χ3122-2-22-12-22-21-22-11-22-2-12-11-211-12-11-2-2-1-2221-111-11-1-221-111-1-12i−2i0000−i3i300−i3i3−i3i3−ii002i−2i00−i−iii000000000000033−3−3000000
χ3222-2-22-12-22-21-22-11-22-2-12-11-211-12-11-2-2-1-2221-111-11-1-221-111-1-12i−2i0000i3−i300i3−i3i3−i3−ii002i−2i00−i−iii0000000000000−3−333000000
χ3322-2-22-12-22-21-22-11-22-2-12-11-211-12-11-2-2-1-2221-111-11-1-221-111-1-1−2i2i0000−i3i300−i3i3−i3i3i−i00−2i2i00ii−i−i0000000000000−3−333000000
χ3422-2-22-12-22-21-22-11-22-2-12-11-211-12-11-2-2-1-2221-111-11-1-221-111-1-1−2i2i0000i3−i300i3−i3i3−i3i−i00−2i2i00ii−i−i000000000000033−3−3000000
χ3522-2-2-122-221-2-2-12-2-221-1-1211-2-2-1-121112-22-1-2-111-11-11-1-2211-1-12i−2i0000000000002i−2i00−ii3−3−i−iii3−33−30000000000000−i3−i3i3i300
χ3622-2-2-122-221-2-2-12-2-221-1-1211-2-2-1-121112-22-1-2-111-11-11-1-2211-1-12i−2i0000000000002i−2i00−ii−33−i−iii−33−330000000000000i3i3−i3−i300
χ3722-2-2-122-221-2-2-12-2-221-1-1211-2-2-1-121112-22-1-2-111-11-11-1-2211-1-1−2i2i000000000000−2i2i00i−i3−3ii−i−i3−33−30000000000000i3i3−i3−i300
χ3822-2-2-122-221-2-2-12-2-221-1-1211-2-2-1-121112-22-1-2-111-11-11-1-2211-1-1−2i2i000000000000−2i2i00i−i−33ii−i−i−33−330000000000000−i3−i3i3i300
χ392-2-2222200222-2-2-2-2-2-2222222-2-2-2-2-2-200000022-2-20000000000002i−2i00000000000000000000000000000−i2i22−22i−2i−i2i2−i2i22−22−200
χ402-2-2222200222-2-2-2-2-2-2222222-2-2-2-2-2-200000022-2-20000000000002i−2i00000000000000000000000000000i2−i2−222i−2ii2−i2i2−i2−22−2200
χ412-2-2222200222-2-2-2-2-2-2222222-2-2-2-2-2-200000022-2-2000000000000−2i2i00000000000000000000000000000−i2i2−22−2i2i−i2i2−i2i2−22−2200
χ422-2-2222200222-2-2-2-2-2-2222222-2-2-2-2-2-200000022-2-2000000000000−2i2i00000000000000000000000000000i2−i22−2−2i2ii2−i2i2−i22−22−200
χ4344444-24-4-44-244-2-2444-24-2-24-2-2-24-2-24-42-4-4-42-2-2-2-222-4-42222220000000000000000000000000000000000000000000000000
χ4444444-2-2444-2-24-2-2-2-24-2-21-2-211-2-21-2-24-2-2-24-21111-2-2-2-2111111000040-2-2-2-2111100000000000000000000000000000000000
χ4544444-2-2444-2-24-2-2-2-24-2-21-2-211-2-21-2-24-2-2-24-21111-2-2-2-21111110000-402222-1-1-1-100000000000000000000000000000000000
χ4644444-2-2-4-44-2-24-2-2-2-24-2-21-2-211-2-21-2-2-4222-4211112222-1-1-1-1-1-100000000−2i32i3i3i3−i3−i300000000000000000000000000000000000
χ4744444-2-2-4-44-2-24-2-2-2-24-2-21-2-211-2-21-2-2-4222-4211112222-1-1-1-1-1-1000000002i3−2i3−i3−i3i3i300000000000000000000000000000000000
χ484444-244-4-4-244-24444-2-2-24-2-244-2-24-2-22-4-4-42-4-2-2-2-22222-4-422220000000000000000000000000000000000000000000000000
χ494444-24-244-24-2-244-2-2-2-21-2-21-2-2-21-2-21-24-2-2-241111-2-211-2-211110000040000000000-2-200-2-2000011110000000000000000000
χ504444-24-244-24-2-244-2-2-2-21-2-21-2-2-21-2-21-24-2-2-241111-2-211-2-2111100000-400000000002200220000-1-1-1-10000000000000000000
χ514444-24-2-4-4-24-2-244-2-2-2-21-2-21-2-2-21-2-212-4222-4111122-1-122-1-1-1-10000000000000000−2i32i300000000i3i3−i3−i30000000000000000000
χ524444-24-2-4-4-24-2-244-2-2-2-21-2-21-2-2-21-2-212-4222-4111122-1-122-1-1-1-100000000000000002i3−2i300000000−i3−i3i3i30000000000000000000
χ534444-2-2444-2-24-2-2-244-21-2-21-2-2-21-2-21-2-2-244-2-2111111-2-2-2-2111144000000000000-2-200-2-200111100000000000000000000000
χ544444-2-2444-2-24-2-2-244-21-2-21-2-2-21-2-21-2-2-244-2-2111111-2-2-2-21111-4-400000000000022002200-1-1-1-100000000000000000000000
χ554444-2-24-4-4-2-24-2-2-244-21-2-21-2-2-21-2-21-222-4-4221111-1-12222-1-1-1-100000000000000000000003-33-300000000000000000000000
χ564444-2-24-4-4-2-24-2-2-244-21-2-21-2-2-21-2-21-222-4-4221111-1-12222-1-1-1-10000000000000000000000-33-3300000000000000000000000
χ5744-4-444-24-4-4-4244-42-2-44-2-2-42224-2-2-424-4-22-44-222-24-4-22-22-2-2220000000000000000000000000000000000000000000000000
χ5844-4-444-2-44-4-4244-42-2-44-2-2-42224-2-2-42-442-24-4-222-2-442-22-222-2-20000000000000000000000000000000000000000000000000
χ5944-4-44-244-4-42-44-22-44-4-24-22-422-24-22-4424-4-4-2-222-2-224-4-22-2-2220000000000000000000000000000000000000000000000000
χ6044-4-44-2-24-4-4224-222-2-4-2-2122-1-1-2-212242-22-4-21-1-11-22-221-111-1-100000000003-3-3300000000000000000000000000000000000
χ6144-4-44-2-24-4-4224-222-2-4-2-2122-1-1-2-212242-22-4-21-1-11-22-221-111-1-10000000000-333-300000000000000000000000000000000000
χ6244-4-44-2-2-44-4224-222-2-4-2-2122-1-1-2-2122-4-22-2421-1-112-22-2-11-1-111000000−2i32i300i3−i3i3−i300000000000000000000000000000000000
χ6344-4-44-2-2-44-4224-222-2-4-2-2122-1-1-2-2122-4-22-2421-1-112-22-2-11-1-1110000002i3−2i300−i3i3−i3i300000000000000000000000000000000000
χ6444-4-4-2444-42-4-4-24-4-442-2-2422-4-4-2-2422-2-44-424-222-2-22-224-4-2-2220000000000000000000000000000000000000000000000000
χ6544-4-4-24-24-42-42-24-42-22-21-22-122-21-22-1-2-4-22241-1-11-221-1-2211-1-1000000000000000000000000003i−3i−3i3i0000000000000000000
χ6644-4-4-24-24-42-42-24-42-22-21-22-122-21-22-1-2-4-22241-1-11-221-1-2211-1-100000000000000000000000000−3i3i3i−3i0000000000000000000
χ6744-4-4-24-2-442-42-24-42-22-21-22-122-21-22-1242-2-2-41-1-112-2-112-2-1-1110000000000000000000023−230000−33−330000000000000000000
χ6844-4-4-24-2-442-42-24-42-22-21-22-122-21-22-1242-2-2-41-1-112-2-112-2-1-11100000000000000000000−232300003−33−30000000000000000000
χ6944-4-4-2-244-422-4-2-22-4421-2-2-12221-2-2-12-224-42-21-1-111-1-22-2211-1-100000000000000000000003i−3i−3i3i00000000000000000000000
χ7044-4-4-2-244-422-4-2-22-4421-2-2-12221-2-2-12-224-42-21-1-111-1-22-2211-1-10000000000000000000000−3i3i3i−3i00000000000000000000000
χ7144-4-4-2-24-4422-4-2-22-4421-2-2-12221-2-2-122-2-44-221-1-11-112-22-2-1-1114i−4i000000000000−2i2i00−2i2i00ii−i−i00000000000000000000000
χ7244-4-4-2-24-4422-4-2-22-4421-2-2-12221-2-2-122-2-44-221-1-11-112-22-2-1-111−4i4i0000000000002i−2i002i−2i00−i−iii00000000000000000000000
χ734-44-444400-4-4-4-4-444-44444-4-4-44-4-4-4440000004-44-400000000000000000000000000000000000000000000000000000000000
χ744-44-444-200-4-42-4-44-2244-2-2-422-2-4224-2000000-22-2200000000000000000000000000000000000000000−2i32i30000000000000000
χ754-44-444-200-4-42-4-44-2244-2-2-422-2-4224-2000000-22-22000000000000000000000000000000000000000002i3−2i30000000000000000
χ764-44-44-2400-42-4-42-24-44-24-22-42-22-42-24000000-22-220000000000000000000000000000000000000000000000000i6−i6−i6i6000000
χ774-44-44-2400-42-4-42-24-44-24-22-42-22-42-24000000-22-220000000000000000000000000000000000000000000000000−i6i6i6−i6000000
χ784-44-4-244002-4-42-444-4-2-2-2422-4422-4-2-2000000-22-2200000000000000000000000000000000000000000000000000000i6−i6−i6i600
χ794-44-4-244002-4-42-444-4-2-2-2422-4422-4-2-2000000-22-2200000000000000000000000000000000000000000000000000000−i6i6i6−i600
χ804-4-4444-20044-2-4-4-422-44-2-24-2-22-422-42000000-2-2220000000000004i−4i000000000000000000000000000000000−2i2i0000000000
χ814-4-4444-20044-2-4-4-422-44-2-24-2-22-422-42000000-2-222000000000000−4i4i0000000000000000000000000000000002i−2i0000000000
χ824-4-444-24004-24-422-4-4-4-24-2-24-222-422-4000000-2-2220000000000000000000000000000000000000000000−2i22i20000i2−i2i2−i2000000
χ834-4-444-24004-24-422-4-4-4-24-2-24-222-422-4000000-2-22200000000000000000000000000000000000000000002i2−2i20000−i2i2−i2i2000000
χ844-4-44-24400-2442-4-4-4-42-2-24-2-24-422-422000000-2-22200000000000000000000000000000000000000000000022−22000000−22−2200
χ854-4-44-24400-2442-4-4-4-42-2-24-2-24-422-422000000-2-222000000000000000000000000000000000000000000000−22220000002−22−200
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
χ8888-8-8-4-4-48-8444-4-444-44222-2-2-2-2222-2-2-44-444-4-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000000
χ8988-8-8-4-4-4-88444-4-444-44222-2-2-2-2222-2-24-44-4-44-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000000
χ908-88-88-4-400-844-84-4-448-4-4244-2244-2-4-40000002-22-200000000000000000000000000000000000000000000000000000000000
χ918-88-8-48-4004-844-88-44-4-42-44-24-44-24-420000002-22-200000000000000000000000000000000000000000000000000000000000
χ928-88-8-4-480044-844-48-8-42-4-4-244-4-2442-40000002-22-200000000000000000000000000000000000000000000000000000000000
χ938-88-8-4-4-40044444-4-44-4222-2-2-22-2-2-222000000-11-1100000033−3333−330000000000000000000000000000000000000000000000000
χ948-88-8-4-4-40044444-4-44-4222-2-2-22-2-2-222000000-11-11000000−3333−33330000000000000000000000000000000000000000000000000
χ958-8-888-4-4008-4-4-84444-8-4-42-4-42-244-24400000022-2-200000000000000000000000000000000000000000000000000000000000
χ968-8-88-48-400-48-44-8-8444-42-4-42-444-244-200000022-2-200000000000000000000000000000000000000000000000000000000000
χ978-8-88-4-4800-4-48444-8-842-4-42-4-44-244-2400000022-2-200000000000000000000000000000000000000000000000000000000000
χ988-8-88-4-4-400-4-4-4444444222222-2-2-2-2-2-2000000-1-11100000033−33−33330000000000000000000000000000000000000000000000000
χ998-8-88-4-4-400-4-4-4444444222222-2-2-2-2-2-2000000-1-111000000−333333−330000000000000000000000000000000000000000000000000

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