Finite Group Databasebeta

← Group #13168053

Character table — Group #13168053

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order1222333666666666333466666666612122236661212121212121212121212122244466666612124466666666612121212121212121212122244466121212121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-11111111-1-1-1-11111111111-1-11-111-1-1-1-11-11-1-111-1-1-1-1-1-1-1-1-11-1
χ311111111111111111111111111111111111111111111111111-111-11111-1-111-1-1-111-1-11111-111-11-1-11111-11-11-1-1-111-1-1-1-1-1-11-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-11111111111111111-11111-1-1-1-11111111-1-111-1-1-1-111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111-1-11111111111111111-11-1-11-1-1-1-111-1-1-1-11-1-111-1-1-1-11-1-11-111-1-1-1-1-11-11-1-1-111-1-1-1-1111-11
χ71111111111111111111111111111111-1-11111111111111111-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111111-11-1-111-1-1-1-1-1-111-111
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-1-11111-1-1-111-1-1-1-1-1-11111-1-1111-1-111-1-1-1-11-11
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111111111111-1-11111-1-1-1-1-1-11-1-111-1-11-1-11-11111-1-11111-1-1-1
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-111-1-1-1-1-111-1-11111-111-1-111-111-1-1-1-1-1-1-1-1111111-1
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-111-1-11-1-1111111-1-1-1-1111-1-11111-1-1-1-1-111
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-111111-1-111-111-1-1-1-1-1-111-1-1111-1-11111-1-111-11-1
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-111111111111-1-111-1-1-1-11-1-111-1-1-111-1-1-1-1-1-1-1-111-1-1111
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-1-1-1-1-111-111-1-1-1-1111111-111-1-1111-1-11-11111-1-111-1-1-1-11
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-111-1-1-111-1-1-1-1111-1-1111111-1-111-1-1111-1-111-1-1111-1-1
χ17222222-12-1-122-12222-1-122-1-1-1-1-12-122222-1-1-1-1-12-1-1-1-122-1-1-1-12200222-1-1-1-1000022-1-1-1-1-1-1-1-10020-1-1000020200-1-1000000000-10
χ18222222-12-1-122-12222-1-122-1-1-1-1-12-122222-1-1-1-1-12-1-1-1-122-1-1-1-12-200-222-1-1110000-22-111-1-1-1-1100-20110000-20-2001100000000010
χ19222222-12-1-122-12222-1-122-1-1-1-1-12-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-22002-2-211-1-100002-21-1-11111-10020-1-10000-20-2001100000000010
χ20222222-12-1-122-12222-1-122-1-1-1-1-12-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-2-200-2-2-211110000-2-21111111100-2011000020200-1-1000000000-10
χ21222222-12-1-122-12222-1-1-22-1-1-1-1-12-12-2-222-1-1-1-11-21111-2-21111-2200-222-1-1-1-100002-21-1-1-1-111100-2011000020-200-1-100000000010
χ22222222-12-1-122-12222-1-1-22-1-1-1-1-12-12-2-222-1-1-1-11-21111-2-21111-2-200222-1-1110000-2-2111-1-111-10020-1-10000-2020011000000000-10
χ23222222-12-1-122-12222-1-1-22-1-1-1-1-12-12-2-2-2-2-1-1-1-11-21111-2-211112200-2-2-211-1-1000022-1-1-111-1-1100-20110000-2020011000000000-10
χ24222222-12-1-122-12222-1-1-22-1-1-1-1-12-12-2-2-2-2-1-1-1-11-21111-2-211112-2002-2-211110000-22-11111-1-1-10020-1-1000020-200-1-100000000010
χ2522222-12-1222-1222-1-12-12-12-1-12-1-12-12222-1-1-1-12-122-1-1-1-1-1-1-1-120220-1-12200-1-1000-1200-1-1-1-102-10200-1-1-1-10202000-1-1000000-100
χ2622222-12-1222-1222-1-12-12-12-1-12-1-12-12222-1-1-1-12-122-1-1-1-1-1-1-1-120-2-20-1-1220011000-1200-1-1-1-10-210-20011110-20-200011000000100
χ2722222-12-1222-1222-1-12-12-12-1-12-1-12-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-2022011-2-200-1-10001-200111102-10200-1-1-1-10-20-200011000000100
χ2822222-12-1222-1222-1-12-12-12-1-12-1-12-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-20-2-2011-2-200110001-20011110-210-20011110202000-1-1000000-100
χ2922222-12-1222-1222-1-12-1-2-12-1-12-1-12-1-2-222-1-1-1-1-21-2-211111111-202-20-1-12200110001-200-1-11102-10-20011-1-1020-200011000000-100
χ3022222-12-1222-1222-1-12-1-2-12-1-12-1-12-1-2-222-1-1-1-1-21-2-211111111-20-220-1-12200-1-10001-200-1-1110-210200-1-1110-202000-1-1000000100
χ3122222-12-1222-1222-1-12-1-2-12-1-12-1-12-1-2-2-2-2-1-1-1-1-21-2-211111111202-2011-2-20011000-120011-1-102-10-20011-1-10-202000-1-1000000100
χ3222222-12-1222-1222-1-12-1-2-12-1-12-1-12-1-2-2-2-2-1-1-1-1-21-2-21111111120-22011-2-200-1-1000-120011-1-10-210200-1-111020-200011000000-100
χ332222-122222-122-1-12-1-122-1-122-12-1-1-1-1-100-1-1-1-122-1-122-1-1-1-1-1-1022220000222222-100-1-100002-12-1-1-1-1-1-1-1-1000020000-1-1-1-100000
χ342222-122222-122-1-12-1-122-1-122-12-1-1-1-1-100-1-1-1-122-1-122-1-1-1-1-1-102-2-22000022-2-2-2-2-100-1-1000021-2-11-1-111110000-20000111100000
χ352222-122222-122-1-12-1-122-1-122-12-1-1-1-1-100-1-1-1-122-1-122-1-1-1-1-1-10-222-20000-2-222-2-2100110000-2-121-111-1-1-1-10000-20000111100000
χ362222-122222-122-1-12-1-122-1-122-12-1-1-1-1-100-1-1-1-122-1-122-1-1-1-1-1-10-2-2-2-20000-2-2-2-222100110000-21-211111111000020000-1-1-1-100000
χ372222-122222-122-1-12-1-12-2-1-122-12-1-1-11100-1-1-1-1-2-211-2-2111111022-2-2000022-2-2-2-2-100-1-10000-2-12111111-1-1000020000-1-11100000
χ382222-122222-122-1-12-1-12-2-1-122-12-1-1-11100-1-1-1-1-2-211-2-211111102-22-20000222222-100-1-10000-21-21-111-1-1110000-2000011-1-100000
χ392222-122222-122-1-12-1-12-2-1-122-12-1-1-11100-1-1-1-1-2-211-2-21111110-22-220000-2-2-2-2221001100002-12-11-1-111-1-10000-2000011-1-100000
χ402222-122222-122-1-12-1-12-2-1-122-12-1-1-11100-1-1-1-1-2-211-2-21111110-2-2220000-2-222-2-210011000021-2-1-1-1-1-1-111000020000-1-11100000
χ4122-2-2222-22-222-2-2-2-22220-2-2-2-222-2-22002-22-2-22000000000000000002-22-200002i−2i000002-20000000000000000000000002i−2i2i−2i000
χ4222-2-2222-22-222-2-2-2-22220-2-2-2-222-2-22002-22-2-22000000000000000002-22-20000−2i2i000002-2000000000000000000000000−2i2i−2i2i000
χ4322-2-2222-22-222-2-2-2-22220-2-2-2-222-2-2200-222-2-2200000000000000000-22-2200002i−2i00000-220000000000000000000000002i−2i−2i2i000
χ4422-2-2222-22-222-2-2-2-22220-2-2-2-222-2-2200-222-2-2200000000000000000-22-220000−2i2i00000-22000000000000000000000000−2i2i2i−2i000
χ4544444-2-2-2-2-24-2-244-2-2-214-2-211-21-2-2-244441111-2-2-2-211-2-2111140000-2-2-2-20000000-2-200111100000000000000000000000000000
χ4644444-2-2-2-2-24-2-244-2-2-214-2-211-21-2-2-244-4-41111-2-2-2-211-2-21111-40000222200000002200-1-1-1-100000000000000000000000000000
χ4744444-2-2-2-2-24-2-244-2-2-21-4-2-211-21-2-2-2-4-44411112222-1-122-1-1-1-1-40000-2-2-2-20000000220011-1-100000000000000000000000000000
χ4844444-2-2-2-2-24-2-244-2-2-21-4-2-211-21-2-2-2-4-4-4-411112222-1-122-1-1-1-14000022220000000-2-200-1-11100000000000000000000000000000
χ494444-24-24-2-2-24-2-2-24-21-24-21-2-21-2-21-2-2-2001111-2411-2-2-2-21111040040000-2-20000-200110000-200-20110000000000000000000000
χ504444-24-24-2-2-24-2-2-24-21-24-21-2-21-2-21-2-2-2001111-2411-2-2-2-211110-400-40000220000200-1-1000020020-1-10000000000000000000000
χ514444-24-24-2-2-24-2-2-24-21-2-4-21-2-21-2-21-2220011112-4-1-12222-1-1-1-10400-40000-2-20000-20011000020020-1-10000000000000000000000
χ524444-24-24-2-2-24-2-2-24-21-2-4-21-2-21-2-21-2220011112-4-1-12222-1-1-1-10-40040000220000200-1-10000-200-20110000000000000000000000
χ534444-2-24-244-2-24-2-2-21-2-241-2-2-2-2-21-21-2-20011114-2-2-2-2-211111100440000000-2-2000000000000-2-20-2001111000000000000000000
χ544444-2-24-244-2-24-2-2-21-2-241-2-2-2-2-21-21-2-20011114-2-2-2-2-211111100-4-4000000022000000000000220200-1-1-1-1000000000000000000
χ554444-2-24-244-2-24-2-2-21-2-2-41-2-2-2-2-21-2122001111-422222-1-1-1-1-1-1004-4000000022000000000000-2-20200-1-111000000000000000000
χ564444-2-24-244-2-24-2-2-21-2-2-41-2-2-2-2-21-2122001111-422222-1-1-1-1-1-100-440000000-2-2000000000000220-20011-1-1000000000000000000
χ5744-4-444-2-4-22442-4-4-44-2-20-4222-2-2-424004-4-222-2000000000000000004-4-2200000000000-220000000000000000000000000000000
χ5844-4-444-2-4-22442-4-4-44-2-20-4222-2-2-42400-44-222-200000000000000000-442-2000000000002-20000000000000000000000000000000
χ5944-4-44-2424-44-2-4-4-42-24-202-4224-22-4-2004-4-222-200000000000000000-224-400000000000-220000000000000000000000000000000
χ6044-4-44-2424-44-2-4-4-42-24-202-4224-22-4-200-44-222-2000000000000000002-2-44000000000002-20000000000000000000000000000000
χ6144-4-44-2-22-224-22-4-42-2-21022-1-1-2122-2004-41-1-1100003-30033-3-300000-22-22000000000001-13-300000000000000000000000000000
χ6244-4-44-2-22-224-22-4-42-2-21022-1-1-2122-2004-41-1-110000-3300-3-33300000-22-22000000000001-1-3300000000000000000000000000000
χ6344-4-44-2-22-224-22-4-42-2-21022-1-1-2122-200-441-1-1100003-30033-3-3000002-22-200000000000-11-3300000000000000000000000000000
χ6444-4-44-2-22-224-22-4-42-2-21022-1-1-2122-200-441-1-110000-3300-3-333000002-22-200000000000-113-300000000000000000000000000000
χ6544-4-4-244-44-4-24-422-4-2-24022-4-4-2422-20000-222-200000000000000000000000004i−4i0000000000000000000000000000000−2i2i00000
χ6644-4-4-244-44-4-24-422-4-2-24022-4-4-2422-20000-222-20000000000000000000000000−4i4i00000000000000000000000000000002i−2i00000
χ674-44-4444-4-4-4-4-444-444440-444-4-4-44-4-4000044-4-400000000000000000000000000000000000000000000000000000000000000000
χ684-44-444-2-422-4-4-24-444-2-20-4-2-222242-40000-2-222000000000000000000000−2i32i30000000−2i32i3000000000000000000000000000000000
χ694-44-444-2-422-4-4-24-444-2-20-4-2-222242-40000-2-2220000000000000000000002i3−2i300000002i3−2i3000000000000000000000000000000000
χ704-44-44-242-4-4-4244-4-2-24-2024-22-42-2-420000-2-22200000000000000000000000−2i32i3000000000000000000−2i32i300000000000000000000
χ714-44-44-242-4-4-4244-4-2-24-2024-22-42-2-420000-2-222000000000000000000000002i3−2i30000000000000000002i3−2i300000000000000000000
χ724-44-4-244-4-4-42-44-224-2-2402-24-42-4-22223−2300-2-2220023−230023−2323−2323−2300000000000000000000000000000000000000000000000000000
χ734-44-4-244-4-4-42-44-224-2-2402-24-42-4-222−232300-2-22200−232300−2323−2323−232300000000000000000000000000000000000000000000000000000
χ744-44-4-24-2-4222-4-2-224-21-2021-22-12-2-1223−230011-1-100−330023−23−33−33000000000−2i32i30000000i3−i30000000003i−3i0000000000000000000000
χ754-44-4-24-2-4222-4-2-224-21-2021-22-12-2-1223−230011-1-100−330023−23−33−330000000002i3−2i30000000−i3i3000000000−3i3i0000000000000000000000
χ764-44-4-24-2-4222-4-2-224-21-2021-22-12-2-12−23230011-1-1003−300−23233−33−3000000000−2i32i30000000i3−i3000000000−3i3i0000000000000000000000
χ774-44-4-24-2-4222-4-2-224-21-2021-22-12-2-12−23230011-1-1003−300−23233−33−30000000002i3−2i30000000−i3i30000000003i−3i0000000000000000000000
χ784-44-4-2-242-4-4224-22-21-2-20-1-2-222212-123−230011-1-10023−2300−33−33−3300000000000−2i32i3000000000000000000i3−i33i−3i000000000000000000
χ794-44-4-2-242-4-4224-22-21-2-20-1-2-222212-123−230011-1-10023−2300−33−33−33000000000002i3−2i3000000000000000000−i3i3−3i3i000000000000000000
χ804-44-4-2-242-4-4224-22-21-2-20-1-2-222212-1−23230011-1-100−2323003−33−33−300000000000−2i32i3000000000000000000i3−i3−3i3i000000000000000000
χ814-44-4-2-242-4-4224-22-21-2-20-1-2-222212-1−23230011-1-100−2323003−33−33−3000000000002i3−2i3000000000000000000−i3i33i−3i000000000000000000
χ824-4-444444-44-4-4-4-44-444404-4-44-4-4-44-400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ834-4-4444-242-2-4-42-44-44-2-20422-222-4-2-40000-22-220000000000000000000000000000000000000000000000000000−2i32i300000000000
χ844-4-4444-242-2-4-42-44-44-2-20422-222-4-2-40000-22-2200000000000000000000000000000000000000000000000000002i3−2i300000000000
χ854-4-444-24-2-44-42-4-442-24-20-2-42-2-422420000-22-2200000000000000000000000000000000000000000000000000000023−23000000000
χ864-4-444-24-2-44-42-4-442-24-20-2-42-2-422420000-22-22000000000000000000000000000000000000000000000000000000−2323000000000
χ874-4-44-2444-442-4-42-2-4-2-240-22-442-42-220000-22-220000000000000000000000000000000000000000000000000000000023−230000000
χ884-4-44-2444-442-4-42-2-4-2-240-22-442-42-220000-22-2200000000000000000000000000000000000000000000000000000000−23230000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-400-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224400-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ9188-8-8-48-4-8-44-48444-8-42-404-2442-44-2-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4848-8-4-4-84442-4-40-2444-4-4-24200002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-44-44-4-444442220-2-2-2-222-2-220000-111-100006-600-3-33300000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-44-4-444442220-2-2-2-222-2-220000-111-10000-660033-3-300000000000000000000000000000000000000000000000000000
χ958-88-88-4-4444-84-48-8-4-4-4204-42-24-2-444000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-444444-4-44-42220-222-2-2-22-2-243−4300-1-11100−232300−23233−33−300000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-444444-4-44-42220-222-2-2-22-2-2−434300-1-1110023−230023−23−33−3300000000000000000000000000000000000000000000000000000
χ988-8-888-4-4-44-4-844-884-4-420-44-224-24-4400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-484-44-844-4-8-42-40-4-24-4-2442400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48-4-8844-84-442-4-40244-444-2-4-200002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4-44-44444-4422202-2-22-2-2-22-20000-11-110000000033−33−333300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4-44-44444-4422202-2-22-2-2-22-20000-11-1100000000−333333−3300000000000000000000000000000000000000000000000000000

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