Finite Group Databasebeta

← Group #13172191

Character table — Group #13172191

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order122233366666666623336666666664436666666666666666444441212121212121212121212124412121212121212121212121212121212121222444661212121222612122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-111-11111-1-11111-1-1-1-11-11-11111111111-1-1-1-11-11-1-1-1-1-1-111-1-11-1-1-1
χ3111111111111111111111111111111111111111111111111-111-1111-1-111-1-11111-1-111-111-11111-1-1-1-11111-11-11-111-1-1-1-1-1-1-1-11-1
χ4111111111111111111111111111111111111111111111111-1-11-1-111-1-1-1-1-1-111-1-1111-1-1-11-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-11-11
χ511111111111111111111111111111-1-11111111111111111111-111-1-1111111-1-11111-1111-11-1-1-1-111111111-1-1-1-11-1-111-1-1-1-1-11-1-1
χ611111111111111111111111111111-1-1111111111111111111-1-11-1-1-111-1-111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-1-11-11-111-1-1-1-111-1-111
χ711111111111111111111111111111-1-111111111111111111-11-1-11-1-1-1-111-1-1-1-111-1-1-11-11-1-1-1-1-1-1-1-1-1-111111-11-1-1-1-1-1-111111-1-11
χ811111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111-1
χ91111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1111111-1-111-1-1-1-1-111-1-1-111-1-111-1-111-1-1-1-1111-1-1-1-111-1-1-1111
χ101111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-111111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-111-111-1-111111111-1-1-1-1
χ111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-111-1-1111111-1-111-11-1-1-1111-1-1-1-11111-1-11-1-11-1-1-111-1-1111-11-1
χ121111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-11-1111-1-1-1-111-1-11111-1-1111-1-1-1-1-1-111-11
χ131111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1111-11-1-1-11111-1-111-1-111-1-1111-1-1-1-11111-1-1
χ141111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-11-11-11-1-111-1-1-1-1-1-111111-1111-1-1-11111-1-1-1-1111-1-11-1-1-111-1-1-1-11-111
χ151111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-11111-1-1-111-1-1111111-1-1-1-1-11
χ161111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-111-1-111-1-11-1-1111-1-111-1-111-1-111-1-1111-1-1-1-11111-111-1
χ17222222-122-1-12222-122-1-12-1-122-1-1-1-122-122-122-1-1-1-1-1-1-1-1-1-1-10220222002200-1-1-1-100-1-10220-1-1-1-10000-1-1-1-102020-1-100000000-10
χ18222222-122-1-12222-122-1-12-1-122-1-1-1-122-122-122-1-1-1-1-1-1-1-1-1-1-10-220-22200-2-200-1-11100-110-220-1-1-1-1000011110-20-20110000000010
χ19222222-122-1-12222-122-1-12-1-122-1-1-1-1-2-2-122-122-1-1-1-1-1-1-1-1-1-1-102-202-2-200220011-1-1001-102-2011110000-1-1-1-10-20-20110000000010
χ20222222-122-1-12222-122-1-12-1-122-1-1-1-1-2-2-122-122-1-1-1-1-1-1-1-1-1-1-10-2-20-2-2-200-2-200111100110-2-2011110000111102020-1-100000000-10
χ21222222-122-1-12222-1-22-1-12-1-122-1-1-1-122-1-2-21-2-21111-1-1-1111102-20-222002200-1-111001-10-2-20-1-1110000-1-1110-20201100000000-10
χ22222222-122-1-12222-1-22-1-12-1-122-1-1-1-122-1-2-21-2-21111-1-1-111110-2-2022200-2-200-1-1-1-1001102-20-1-111000011-1-1020-20-1-10000000010
χ23222222-122-1-12222-1-22-1-12-1-122-1-1-1-1-2-2-1-2-21-2-21111-1-1-111110220-2-2-2002200111100-1-10-22011-1-10000-1-111020-20-1-10000000010
χ24222222-122-1-12222-1-22-1-12-1-122-1-1-1-1-2-2-1-2-21-2-21111-1-1-111110-2202-2-200-2-20011-1-100-11022011-1-1000011-1-10-20201100000000-10
χ2522222-12-1-122222-122-12-1-12-1-1-122-1-122-12-12-1-122-1-1-1-1-1-1-1-1-120220-1-1-1-100222200002020-1-1-1-1-1-1-1-1-1-10000202000000-1-100-1000
χ2622222-12-1-122222-122-12-1-12-1-1-122-1-122-12-12-1-122-1-1-1-1-1-1-1-1-1-202-20-1-11100-2-222000020-20-11-1-1-1-111110000-20-200000011001000
χ2722222-12-1-122222-122-12-1-12-1-1-122-1-1-2-2-12-12-1-122-1-1-1-1-1-1-1-1-120-22011-1-10022-2-20000-20201-11111-1-1-1-10000-20-200000011001000
χ2822222-12-1-122222-122-12-1-12-1-1-122-1-1-2-2-12-12-1-122-1-1-1-1-1-1-1-1-1-20-2-20111100-2-2-2-20000-20-2011111111110000202000000-1-100-1000
χ2922222-12-1-122222-12-2-12-1-12-1-1-122-1-122-1-21-211-2-211-1-1-1111120-2-20-1-1-1-100-2-2220000-202011-1-111-1-1110000-202000000-1-1001000
χ3022222-12-1-122222-12-2-12-1-12-1-1-122-1-122-1-21-211-2-211-1-1-11111-20-220-1-1110022220000-20-201-1-1-11111-1-1000020-20000001100-1000
χ3122222-12-1-122222-12-2-12-1-12-1-1-122-1-1-2-2-1-21-211-2-211-1-1-11111202-2011-1-100-2-2-2-200002020-1111-1-1-1-111000020-20000001100-1000
χ3222222-12-1-122222-12-2-12-1-12-1-1-122-1-1-2-2-1-21-211-2-211-1-1-11111-2022011110022-2-2000020-20-1-111-1-111-1-10000-202000000-1-1001000
χ332222-1222222-1-1-1222-1-12-1-12-1-1-1-12200-1-122-1-1-1-122-1-1-1-1-1-1-1220220022-1-1-1-100222202-1-1020000-1-1-1-1-1-1-1-10000200-1-100000-100
χ342222-1222222-1-1-1222-1-12-1-12-1-1-1-12200-1-122-1-1-1-122-1-1-1-1-1-1-12-202-2002211-1-100-2-2-2-20-2-11020000-1-1-1-111110000-2001100000100
χ352222-1222222-1-1-1222-1-12-1-12-1-1-1-12200-1-122-1-1-1-122-1-1-1-1-1-1-1-220-2200-2-2-1-1110022-2-2021-10-200001111-1-1-1-10000-2001100000100
χ362222-1222222-1-1-1222-1-12-1-12-1-1-1-12200-1-122-1-1-1-122-1-1-1-1-1-1-1-2-20-2-200-2-2111100-2-2220-2110-20000111111110000200-1-100000-100
χ372222-1222222-1-1-122-2-1-12-1-12-1-1-1-12200-11-2-21111-2-2-1-1-11111220-2-20022-1-11100-2-2-2-202-110-20000-1-111-1-11100002001100000-100
χ382222-1222222-1-1-122-2-1-12-1-12-1-1-1-12200-11-2-21111-2-2-1-1-111112-20-22002211110022220-2-1-10-20000-1-11111-1-10000-200-1-100000100
χ392222-1222222-1-1-122-2-1-12-1-12-1-1-1-12200-11-2-21111-2-2-1-1-11111-2202-200-2-2-1-1-1-100-2-222021102000011-1-1-1-1110000-200-1-100000100
χ402222-1222222-1-1-122-2-1-12-1-12-1-1-1-12200-11-2-21111-2-2-1-1-11111-2-202200-2-211-1-10022-2-20-21-102000011-1-111-1-100002001100000-100
χ4122-2-22222-22-22-2-2-2-20222-2-222-22-2-2-22i−2i20000000002-2-20000000002i−2i0000002i−2i002i−2i0000002i−2i000000000000000002i−2i002-20000
χ4222-2-22222-22-22-2-2-2-20222-2-222-22-2-2-22i−2i20000000002-2-20000000002i−2i0000002i−2i00−2i2i0000002i−2i00000000000000000−2i2i00-220000
χ4322-2-22222-22-22-2-2-2-20222-2-222-22-2-2-2−2i2i20000000002-2-2000000000−2i2i000000−2i2i002i−2i000000−2i2i000000000000000002i−2i00-220000
χ4422-2-22222-22-22-2-2-2-20222-2-222-22-2-2-2−2i2i20000000002-2-2000000000−2i2i000000−2i2i00−2i2i000000−2i2i00000000000000000−2i2i002-20000
χ4544444-2-2-2-2-2-2444-2-24-2-21-2-21-2-2-2-2114414-2-2-2-2-2-211111111100400-2-2000000-2-20000-2000-2011110000000000000000000000000
χ4644444-2-2-2-2-2-2444-2-24-2-21-2-21-2-2-2-211-4-414-2-2-2-2-2-211111111100-40022000000220000200020-1-1-1-10000000000000000000000000
χ4744444-2-2-2-2-2-2444-2-2-4-2-21-2-21-2-2-2-211441-4222222-1-1111-1-1-1-100-400-2-2000000-2-2000020002011-1-10000000000000000000000000
χ4844444-2-2-2-2-2-2444-2-2-4-2-21-2-21-2-2-2-211-4-41-4222222-1-1111-1-1-1-10040022000000220000-2000-20-1-1110000000000000000000000000
χ494444-24-244-2-2-2-2-24-24-21-2-21-2-2-211-2-2001-24-2-2-211-2-21111111040040000-2-20000-2-2000-20-20000000000111100000000000000000
χ504444-24-244-2-2-2-2-24-24-21-2-21-2-2-211-2-2001-24-2-2-211-2-211111110-400-40000220000220002020000000000-1-1-1-100000000000000000
χ514444-24-244-2-2-2-2-24-2-4-21-2-21-2-2-211-2-20012-4222-1-122111-1-1-1-10400-40000-2-2000022000-202000000000011-1-100000000000000000
χ524444-24-244-2-2-2-2-24-2-4-21-2-21-2-2-211-2-20012-4222-1-122111-1-1-1-10-40040000220000-2-200020-20000000000-1-11100000000000000000
χ534444-2-24-2-244-2-2-2-2441-2-21-2-211-2-2-2-2001-2-2411-2-2-2-211111114004000-2-200-2-200000000-200-200001111000000000000000000000
χ544444-2-24-2-244-2-2-2-2441-2-21-2-211-2-2-2-2001-2-2411-2-2-2-21111111-400-40002200220000000020020000-1-1-1-1000000000000000000000
χ554444-2-24-2-244-2-2-2-24-41-2-21-2-211-2-2-2-200122-4-1-12222111-1-1-1-1400-4000-2-2002200000000-2002000011-1-1000000000000000000000
χ564444-2-24-2-244-2-2-2-24-41-2-21-2-211-2-2-2-200122-4-1-12222111-1-1-1-1-40040002200-2-200000000200-20000-1-111000000000000000000000
χ5744-4-444-24-4-224-4-4-4204-2-2-42-24-4-22224i−4i-2000000000-2220000000004i−4i000000−2i2i0000000000−2i2i000000000000000000000000000
χ5844-4-444-24-4-224-4-4-4204-2-2-42-24-4-2222−4i4i-2000000000-222000000000−4i4i0000002i−2i00000000002i−2i000000000000000000000000000
χ5944-4-44-24-224-44-4-42-40-24-22-4-2-224-4224i−4i-2000000000-222000000000−2i2i0000004i−4i0000000000−2i2i000000000000000000000000000
χ6044-4-44-24-224-44-4-42-40-24-22-4-2-224-422−4i4i-2000000000-2220000000002i−2i000000−4i4i00000000002i−2i000000000000000000000000000
χ6144-4-44-2-2-22-224-4-4220-2-21221-22-22-1-14i−4i100000003-31-1-133-3-300000−2i2i000000−2i2i0000000000i−i3i−3i0000000000000000000000000
χ6244-4-44-2-2-22-224-4-4220-2-21221-22-22-1-14i−4i10000000-331-1-1-3-33300000−2i2i000000−2i2i0000000000i−i−3i3i0000000000000000000000000
χ6344-4-44-2-2-22-224-4-4220-2-21221-22-22-1-1−4i4i100000003-31-1-133-3-3000002i−2i0000002i−2i0000000000−ii−3i3i0000000000000000000000000
χ6444-4-44-2-2-22-224-4-4220-2-21221-22-22-1-1−4i4i10000000-331-1-1-3-333000002i−2i0000002i−2i0000000000−ii3i−3i0000000000000000000000000
χ6544-4-4-2444-44-4-222-4-40-2-24224-22-22-4-400-2000000000-2220000000000000000000004i−4i0000000000000000000000000−2i2i00000000
χ6644-4-4-2444-44-4-222-4-40-2-24224-22-22-4-400-2000000000-222000000000000000000000−4i4i00000000000000000000000002i−2i00000000
χ674-44-4444-44-4-4-44-4-4404444-4-4-4-4-444-4004000000000-44-40000000000000000000000000000000000000000000000000000000000
χ684-44-444-2-4422-44-4-4-204-2-2422-4-42-2-2200-20000000002-220000000000000000000000000000000000000000000000−2i32i30000000000
χ694-44-444-2-4422-44-4-4-204-2-2422-4-42-2-2200-20000000002-2200000000000000000000000000000000000000000000002i3−2i30000000000
χ704-44-44-242-2-4-4-44-4240-24-2-2-4222-44-2200-20000000002-220000000000023−230000000000000000000023−2300000000000000000000000
χ714-44-44-242-2-4-4-44-4240-24-2-2-4222-44-2200-20000000002-2200000000000−232300000000000000000000−232300000000000000000000000
χ724-44-4-244-44-4-42-22-440-2-24-22-4222-24-400-20000000002-2200000000000000023−2300000000000000000023−23000000000000000000000
χ734-44-4-244-44-4-42-22-440-2-24-22-4222-24-400-20000000002-22000000000000000−2323000000000000000000−2323000000000000000000000
χ744-44-4-2-242-2-4-42-222401-2-2122-1-12-2-220010003-30000-11-13-33-3000000023−230023−230000000000000000−33−33000000000000000000000
χ754-44-4-2-242-2-4-42-222401-2-2122-1-12-2-220010003-30000-11-13-33-30000000−232300−232300000000000000003−33−3000000000000000000000
χ764-44-4-2-242-2-4-42-222401-2-2122-1-12-2-22001000-330000-11-1-33-33000000023−2300−23230000000000000000−333−3000000000000000000000
χ774-44-4-2-242-2-4-42-222401-2-2122-1-12-2-22001000-330000-11-1-33-330000000−23230023−2300000000000000003−3−33000000000000000000000
χ784-4-44444-4-4-44-4-444-40444-44-4-44-4-4-44004000000000-4-440000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-4-42-2-4-444204-2-2-4-22-44222-200-200000000022-2000000000000000000023−2300000000000000000023−2300000000000000000
χ804-4-4444-2-4-42-2-4-444204-2-2-4-22-44222-200-200000000022-20000000000000000000−2323000000000000000000−232300000000000000000
χ814-4-444-2422-44-4-44-2-40-24-22422-2-4-42-200-200000000022-200000000000000000000000000000000000000000000000000−2i32i3000000
χ824-4-444-2422-44-4-44-2-40-24-22422-2-4-42-200-200000000022-2000000000000000000000000000000000000000000000000002i3−2i3000000
χ834-4-44-244-4-4-4422-24-40-2-242-2-42-222-4400-200000000022-2000000000000023−23000000000000000000000023−230000000000000000000
χ844-4-44-244-4-4-4422-24-40-2-242-2-42-222-4400-200000000022-20000000000000−23230000000000000000000000−23230000000000000000000
χ854-4-44-24-2-4-42-222-2420-21-22122-2-1-12-2001000003-300-1-113-3-3300000000023−23000023−230000000000000000−33−3300000000000000000
χ864-4-44-24-2-4-42-222-2420-21-22122-2-1-12-2001000003-300-1-113-3-33000000000−23230000−232300000000000000003−33−300000000000000000
χ874-4-44-24-2-4-42-222-2420-21-22122-2-1-12-200100000-3300-1-11-333-300000000023−230000−23230000000000000000−333−300000000000000000
χ884-4-44-24-2-4-42-222-2420-21-22122-2-1-12-200100000-3300-1-11-333-3000000000−2323000023−2300000000000000003−3−3300000000000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-4822222222222200-1-4-4-4222222-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4-822222222222200-1444-2-2-2-2-2-2-1-1-11111000000000000000000000000000000000000000000000000000000
χ9188-8-8-48-48-8-44-444-840-42-44-2-4-442-2440020000000002-2-20000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48-448-8-4444-802-4-4-24-42-2-44440020000000002-2-20000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-44-44-444440222-2-222-22-2-2-200-100000006-6-111-3-333000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-44-44-444440222-2-222-22-2-2-200-10000000-66-11133-3-3000000000000000000000000000000000000000000000000000000
χ958-88-88-4-44-444-88-84-40-4-42-44-2444-42-2002000000000-22-20000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-4-88444-44-8-40-42-4-4-2444-22-44002000000000-22-20000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44-4444-444-402222-2-2-2-2-222-200-10006-600001-11-33-33000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44-4444-444-402222-2-2-2-2-222-200-1000-6600001-113-33-3000000000000000000000000000000000000000000000000000000
χ998-8-888-4-4444-4-8-88-440-4-424-4-24-444-22002000000000-2-220000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4844-8844-4-4-802-4-4-2-44-22444-4002000000000-2-220000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-444-4-440222-22-2-22-2-2-2200-1000006-60011-1-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-444-4-440222-22-2-22-2-2-2200-100000-660011-13-3-33000000000000000000000000000000000000000000000000000000

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