Finite Group Databasebeta

← Group #13172127

Character table — Group #13172127

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order1222333666666666233366666666666366666666666666622444466121212121212444444666666612121212121212121212121212244121212121212121261224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-111-1111111-1-111-1-1-1-11111111-1-1-1111111-1-1-1-11-1-111-1-1-1-1-1-11-1-1-1
χ3111111111111111111111111111111111111111111111111-111-11-1-111-1-111-1-111-1-111-111-1-1111-1111-1-11111-11-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1111
χ511111111111111111111111111111111111111111111111-111-11111-1-11111-1-1-1-111-1-11-1-1111111-1-1-1111111-1-11-1-111-1-1-1-1-11-1-1
χ611111111111111111111111111111111111111111111111-11-1-11-111-1-111-1-1-1-111-1-1-1-11-1-111-1-1-11-1-1-111-1-1-1-1-11-1-1-1-1-11111-1-111
χ711111111111111111111111111111111111111111111111-1-11-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111-1-111-1-1-1-1-1-11-111
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-111-1-1-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-111-1-1-11111-1-111-1-1-111-1
χ101111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1111-1-1-1-1111111111111111-1-11-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-1-11
χ111111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-11-11-1-1-1-1-111-1-1-1-1-1-11111-111-1-111-11-1-1-11111-1-111-1-1-11111-1-11-1-11
χ121111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-111-1-1-1-11111-1-111-1-111-111-1-1-1-111-1-1-111-1-1111-11-1-1-1-1-1-111111-1
χ131111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1-1-11-1-11111-1-1111-1-111-1-11-11-1-1-1-1-1-11111-11
χ141111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-111111-1-111-1-1-1-111-1-11-1-111-1-11-1111-1-1-1-11111-1-1-11111-1-11-11-1
χ151111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-11111-1-1111111-1-1-1-1-1-1-111-111111111-1-1-1-1-11111-1-111-1-11-1
χ161111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-11111-1-111-1-1-11-11
χ17222222-1222-1-12-12222-1-1222-1-1-1-122-1-1-12-122-1-1-1-1-1-1-1-1-1-1-122022022-1-1-1-1002200002-1-1-1-1-1-100022-1-1-1-10000200-1-1000000-1000
χ18222222-1222-1-12-12222-1-1222-1-1-1-122-1-1-12-122-1-1-1-1-1-1-1-1-1-1-12-202-20-2-2-1-11100-2-200002-11-1-111000-22-1-1110000-200110000001000
χ19222222-1222-1-12-12222-1-1222-1-1-1-122-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1-220-2202211-1-100-2-20000-21-111-1-10002-211-1-10000-200110000001000
χ20222222-1222-1-12-12222-1-1222-1-1-1-122-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1-2-20-2-20-2-2111100220000-2111111000-2-211110000200-1-1000000-1000
χ21222222-1222-1-12-122-22-1-1-2-22-1-1-1-122-1-1-1-21-2-21111-1-1-11111220-2-20221111002200002-1-1-1-1-1-1000-2-211110000-200-1-10000001000
χ22222222-1222-1-12-122-22-1-1-2-22-1-1-1-122-1-1-1-21-2-21111-1-1-111112-20-220-2-211-1-100-2-200002-11-1-1110002-211-1-1000020011000000-1000
χ23222222-1222-1-12-122-22-1-1-2-22-1-1-1-122-1-1-1-21-2-21111-1-1-11111-2202-2022-1-11100-2-20000-21-111-1-1000-22-1-111000020011000000-1000
χ24222222-1222-1-12-122-22-1-1-2-22-1-1-1-122-1-1-1-21-2-21111-1-1-11111-2-20220-2-2-1-1-1-100220000-211111100022-1-1-1-10000-200-1-10000001000
χ2522222-1222-122-12-122-12-122-122-1-1-1-12-1-1-12-1-122-1-1-1-1-1-1-1-1-1022022-1-10022-1-100002200200-1-12-12-1000-1-1-1-1-1-100200-1-100000-100
χ2622222-1222-122-12-122-12-122-122-1-1-1-12-1-1-12-1-122-1-1-1-1-1-1-1-1-102-202-2-1-10022110000-2-200200-1-1-21-2-1000-1-1111100-2001100000100
χ2722222-1222-122-12-122-12-122-122-1-1-1-12-1-1-12-1-122-1-1-1-1-1-1-1-1-10-220-221100-2-2-1-10000-2-200-200112-12100011-1-1-1-100-2001100000100
χ2822222-1222-122-12-122-12-122-122-1-1-1-12-1-1-12-1-122-1-1-1-1-1-1-1-1-10-2-20-2-21100-2-21100002200-20011-21-2100011111100200-1-100000-100
χ2922222-1222-122-12-12-2-12-1-2-2-122-1-1-1-12-1-11-211-2-211-1-1-111110220-2-2-1-100-2-2110000-2-200200-1-12-1-2100011-1-111002001100000-100
χ3022222-1222-122-12-12-2-12-1-2-2-122-1-1-1-12-1-11-211-2-211-1-1-1111102-20-22-1-100-2-2-1-100002200200-1-1-21210001111-1-100-200-1-100000100
χ3122222-1222-122-12-12-2-12-1-2-2-122-1-1-1-12-1-11-211-2-211-1-1-111110-2202-21100221100002200-200112-1-2-1000-1-1-1-11100-200-1-100000100
χ3222222-1222-122-12-12-2-12-1-2-2-122-1-1-1-12-1-11-211-2-211-1-1-111110-2-2022110022-1-10000-2-200-20011-212-1000-1-111-1-1002001100000-100
χ332222-122-1-1222222-12-1-12-1-1-1-1-122-1-1-12-122-1-1-1-122-1-1-1-1-1-1-120220200220022002200-120-1-100-12-10-1-1-100-1-1-1-10200000-1-1-1-10000
χ342222-122-1-1222222-12-1-12-1-1-1-1-122-1-1-12-122-1-1-1-122-1-1-1-1-1-1-120-220-2002200-2-200-2-200-120-1-1001-210-1-1-10011110-20000011110000
χ352222-122-1-1222222-12-1-12-1-1-1-1-122-1-1-12-122-1-1-1-122-1-1-1-1-1-1-1-202-20200-2-2002200-2-2001-201100-12-1011100-1-1-1-10-20000011110000
χ362222-122-1-1222222-12-1-12-1-1-1-1-122-1-1-12-122-1-1-1-122-1-1-1-1-1-1-1-20-2-20-200-2-200-2-20022001-2011001-2101110011110200000-1-1-1-10000
χ372222-122-1-1222222-1-2-1-1211-1-1-122-1-1-12-1-2-21111-2-2-1-1-11111202-20-200-2-200-2-200-2-200-120-1-100-121011100-1-1110200000-1-1110000
χ382222-122-1-1222222-1-2-1-1211-1-1-122-1-1-12-1-2-21111-2-2-1-1-1111120-2-20200-2-20022002200-120-1-1001-2-101110011-1-10-20000011-1-10000
χ392222-122-1-1222222-1-2-1-1211-1-1-122-1-1-12-1-2-21111-2-2-1-1-11111-20220-2002200-2-20022001-201100-1210-1-1-100-1-1110-20000011-1-10000
χ402222-122-1-1222222-1-2-1-1211-1-1-122-1-1-12-1-2-21111-2-2-1-1-11111-20-22020022002200-2-2001-2011001-2-10-1-1-10011-1-10200000-1-1110000
χ4122-2-22222-22-2-2-22-2-2022200-22-22-22-2-2-22000000002-2-20000000000000000002-22i−2i2i−2i000000000000000000000002-22i−2i002i−2i0000
χ4222-2-22222-22-2-2-22-2-2022200-22-22-22-2-2-22000000002-2-20000000000000000002-2−2i2i−2i2i000000000000000000000002-2−2i2i00−2i2i0000
χ4322-2-22222-22-2-2-22-2-2022200-22-22-22-2-2-22000000002-2-2000000000000000000-222i−2i−2i2i00000000000000000000000-22−2i2i002i−2i0000
χ4422-2-22222-22-2-2-22-2-2022200-22-22-22-2-2-22000000002-2-2000000000000000000-22−2i2i2i−2i00000000000000000000000-222i−2i00−2i2i0000
χ4544444-2-244-2-2-2-2-2-244-2-2144-2-2-211-2-2-211-2-2-2-2-2-2111111111040040-2-200-2-20000000000-20011000-2000110000000000000000000
χ4644444-2-244-2-2-2-2-2-244-2-2144-2-2-211-2-2-211-2-2-2-2-2-21111111110-400-402200220000000000200-1-10002000-1-10000000000000000000
χ4744444-2-244-2-2-2-2-2-24-4-2-21-4-4-2-2-211-2-2-211222222-1-1111-1-1-1-10400-40-2-200220000000000-200110002000-1-10000000000000000000
χ4844444-2-244-2-2-2-2-2-24-4-2-21-4-4-2-2-211-2-2-211222222-1-1111-1-1-1-10-400402200-2-20000000000200-1-1000-2000110000000000000000000
χ494444-24-2-2-24-2-24-24-24-21-2-2-2-211-2-2-2-21-214-2-2-211-2-2111111140040000-2-20000000000-2-2011000000-211000000000000000000000
χ504444-24-2-2-24-2-24-24-24-21-2-2-2-211-2-2-2-21-214-2-2-211-2-21111111-400-40000220000000000220-1-10000002-1-1000000000000000000000
χ514444-24-2-2-24-2-24-24-2-4-21-222-211-2-2-2-21-21-4222-1-122111-1-1-1-1400-40000220000000000-2-20110000002-1-1000000000000000000000
χ524444-24-2-2-24-2-24-24-2-4-21-222-211-2-2-2-21-21-4222-1-122111-1-1-1-1-40040000-2-20000000000220-1-1000000-211000000000000000000000
χ534444-2-24-2-2-244-24-2-241-2-2-2-21-2-2-2-211-2-21-2411-2-2-2-21111111004004000000-2-20000000000000-2-2-20000001111000000000000000
χ544444-2-24-2-2-244-24-2-241-2-2-2-21-2-2-2-211-2-21-2411-2-2-2-2111111100-400-4000000220000000000000222000000-1-1-1-1000000000000000
χ554444-2-24-2-2-244-24-2-2-41-2-2221-2-2-2-211-2-212-4-1-12222111-1-1-1-100400-4000000220000000000000-2-2200000011-1-1000000000000000
χ564444-2-24-2-2-244-24-2-2-41-2-2221-2-2-2-211-2-212-4-1-12222111-1-1-1-100-4004000000-2-2000000000000022-2000000-1-111000000000000000
χ5744-4-444-24-4422-4-2-4-404-2-200-4-22-224-422-200000000-2220000000000000000004-4000000000000000000000000000-220000000000
χ5844-4-444-24-4422-4-2-4-404-2-200-4-22-224-422-200000000-222000000000000000000-440000000000000000000000000002-20000000000
χ5944-4-44-244-4-2-4-4242-40-24-20024-4-22-22-42-200000000-22200000000000000000000004i−4i0000000000000000000000000−2i2i00000000
χ6044-4-44-244-4-2-4-4242-40-24-20024-4-22-22-42-200000000-2220000000000000000000000−4i4i00000000000000000000000002i−2i00000000
χ6144-4-4-244-224-4-4-44-420-2-24002-224-4-222-4-200000000-222000000000000000000004i−4i0000000000000000000000000000000−2i2i0000
χ6244-4-4-244-224-4-4-44-420-2-24002-224-4-222-4-200000000-22200000000000000000000−4i4i00000000000000000000000000000002i−2i0000
χ634-44-4444-4-4-44-44-4-440444004-4-4-44-4-44-4400000000-44-400000000000000000000000000000000000000000000000000000000000
χ644-44-444-2-4-4-4-2242-4404-2-2004222-2-4-4-22-2000000002-22000000000000−2i32i30000000000000000000000−2i32i3000000000000000000000
χ654-44-444-2-4-4-4-2242-4404-2-2004222-2-4-4-22-2000000002-220000000000002i3−2i300000000000000000000002i3−2i3000000000000000000000
χ664-44-44-24-4-424-4-2-4240-24-200-2-4-42-22242-2000000002-22000000000000000023−2300000000000000000000000023−23000000000000000
χ674-44-44-24-4-424-4-2-4240-24-200-2-4-42-22242-2000000002-220000000000000000−2323000000000000000000000000−2323000000000000000
χ684-44-4-24422-44-44-4-4-20-2-24−2i32i3-222-4422-2-4-200−2i32i3−2i32i3002-22−2i3−2i32i32i30000000000000000000000000000000000000000000000000000000
χ694-44-4-24422-44-44-4-4-20-2-242i3−2i3-222-4422-2-4-2002i3−2i32i3−2i3002-222i32i3−2i3−2i30000000000000000000000000000000000000000000000000000000
χ704-44-4-24-222-4-2242-4-20-21-2−2i32i3-2-1-12-22212100−2i32i3i3−i300-11-1i3i3−i3−i300000000−2i32i300000000000003-30000000i3−i3000000000000000000000
χ714-44-4-24-222-4-2242-4-20-21-2−2i32i3-2-1-12-22212100−2i32i3i3−i300-11-1i3i3−i3−i3000000002i3−2i30000000000000-330000000−i3i3000000000000000000000
χ724-44-4-24-222-4-2242-4-20-21-22i3−2i3-2-1-12-222121002i3−2i3−i3i300-11-1−i3−i3i3i300000000−2i32i30000000000000-330000000i3−i3000000000000000000000
χ734-44-4-24-222-4-2242-4-20-21-22i3−2i3-2-1-12-222121002i3−2i3−i3i300-11-1−i3−i3i3i3000000002i3−2i300000000000003-30000000−i3i3000000000000000000000
χ744-44-4-2-242224-4-2-42-201-2-2−2i32i31222-2-1-1-22100i3−i3−2i32i300-11-1i3i3−i3−i300000000000023−2300000000000000000000003i−3i−33000000000000000
χ754-44-4-2-242224-4-2-42-201-2-2−2i32i31222-2-1-1-22100i3−i3−2i32i300-11-1i3i3−i3−i3000000000000−23230000000000000000000000−3i3i3−3000000000000000
χ764-44-4-2-242224-4-2-42-201-2-22i3−2i31222-2-1-1-22100−i3i32i3−2i300-11-1−i3−i3i3i300000000000023−230000000000000000000000−3i3i−33000000000000000
χ774-44-4-2-242224-4-2-42-201-2-22i3−2i31222-2-1-1-22100−i3i32i3−2i300-11-1−i3−i3i3i3000000000000−232300000000000000000000003i−3i3−3000000000000000
χ784-4-44444-44-4-44-4-44-4044400-4-44-4-4-44-44400000000-4-4400000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-44-42-2-424-404-2-200-42-222-442-2-20000000022-200000000000000−2i32i30000000000000000000000−2i32i30000000000000000000
χ804-4-4444-2-44-42-2-424-404-2-200-42-222-442-2-20000000022-2000000000000002i3−2i300000000000000000000002i3−2i30000000000000000000
χ814-4-444-24-442-442-4-2-40-24-2002-44222-2-4-2-20000000022-20000000000−2i32i300000000000000000−2i32i30000000000000000000000000000
χ824-4-444-24-442-442-4-2-40-24-2002-44222-2-4-2-20000000022-200000000002i3−2i3000000000000000002i3−2i30000000000000000000000000000
χ834-4-444-2-2-4422-222-2-40-2-210022-2-1-12-22110000003-3-1-113-33-3000000−2i32i300−2i32i30000000000000i3−i30000000i3−i30000000000000000000
χ844-4-444-2-2-4422-222-2-40-2-210022-2-1-12-22110000003-3-1-113-33-30000002i3−2i3002i3−2i30000000000000−i3i30000000−i3i30000000000000000000
χ854-4-444-2-2-4422-222-2-40-2-210022-2-1-12-2211000000-33-1-11-33-33000000−2i32i3002i3−2i30000000000000i3−i30000000−i3i30000000000000000000
χ864-4-444-2-2-4422-222-2-40-2-210022-2-1-12-2211000000-33-1-11-33-330000002i3−2i300−2i32i30000000000000−i3i30000000i3−i30000000000000000000
χ874-4-44-2442-2-4-44-4-4420-2-240022-2-4-42-224-20000000022-200000000000000000000000000000000000000000000000000023−23000000
χ884-4-44-2442-2-4-44-4-4420-2-240022-2-4-42-224-20000000022-2000000000000000000000000000000000000000000000000000−2323000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4222222222-1-4-4222222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4-822244222222222-144-2-2-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000000
χ9188-8-88-4-48-8-4444-44-80-4-42004-442-2-444-22000000002-2-200000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-4-44844-8-4-840-42-40042-2-44-44-242000000002-2-200000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-48-44-4-8-8484402-4-400-2-44-442-2442000000002-2-200000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-44-4444-444022200-22-22-22-2-2-2-100000000-111−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-4-44-4444-444022200-22-22-22-2-2-2-100000000-1113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000
χ968-88-88-4-4-8-84-44-44480-4-4200-444-2244-4-2200000000-22-200000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4444-44-444-40222−4i34i32-2-2-22-2-22-2-1002i3−2i32i3−2i3001-11−i3−i3i3i30000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4444-44-444-402224i3−4i32-2-2-22-2-22-2-100−2i32i3−2i32i3001-11i3i3−i3−i30000000000000000000000000000000000000000000000000000000
χ998-8-88-48-44-4-84-4-84840-42-4004-22444-4-2-4200000000-2-2200000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-484-44-884-8-4402-4-400-24-444-224-4200000000-2-2200000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44-444-444-44022200-2-22-2-2-22-22-10000006-611-1-33-330000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44-444-444-44022200-2-22-2-2-22-22-1000000-6611-13-33-30000000000000000000000000000000000000000000000000000000

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