Finite Group Databasebeta

← Group #13171575

Character table — Group #13171575

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1122222224444444444666666888888889999991212121212121212121212121212121616161616161818181818181818182424242424242424242424243636363636364848485454727272108
order12333466623336661212128888883666612121222444422424242424242424242424242466666122246612121212666612122424242424242446612661288612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-11111111111-1-1-1-111-111111111-1-1-1-1111111-1-1111-1-1-1-11111-1-11111-1-11-1-1-1-1111-1-1-11-1-1-1
χ3111111111111111111111-1-11111111111-1-111-1-11-111111-1-1-1-111111111111-1-1-1-111-1-11-11-11111-1-111-11-11-1-11-11-1-1-11-1-1
χ4111111111111111111111-1-1-1-111111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1111111-11-1-1-1-1-1111-11-1-1-111-1-1-1-1-1-11-11-11-1-111-1-111
χ51111111111111111111-1-1111111111111-1-1-1-111-111-1-1-1-111111111111111-11-1-1-1-1-111-11-1111-1-11111-1-11-11-1-111-1-1-1-11-1
χ61111111111111111111-1-111-1-111111111-1-111-1-1-11-1-1-1-1-11111-1-1-1-11111111-1-1-1-111-1-1-11-11-1-1-1-111-1-1-11-11-1-1-11-111-11-11
χ71111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-11-1-11111-1-11
χ81111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1
χ9111111111-11111111111111111-1-1-11111111111-1-1-1111111111111-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1111-1-1-111-1-1-1-1
χ10111111111-11111111111111-1-11-1-1-1111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-1111111-1-1-111-1-11-1-11-1-1-1111
χ11111111111-111111111111-1-1111-1-1-11111-1-111-1-1-11-11111-1-1-1-11111-1-1-1-1-111-1-1-1-111-1-1-11-11-1-111-1-1111-111-1-1-11-1-1-11-111
χ12111111111-111111111111-1-1-1-11-1-1-11111-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-111-11-111111-1-1-1-111-1-11-1-1111111-1-1
χ13111111111-1111111111-1-111111-1-1-11111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-11-11-1-1-1-1-1111-11-1-1-1-1-1111111-1-11-11-1-1-1-111-11
χ14111111111-1111111111-1-111-1-11-1-1-11111-1-111-1-11-11-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11-11-111-1-111-1-11-111-1-11-11111-11-1
χ15111111111-1111111111-1-1-1-1111-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1111-1-1-1-11111-1-1-1-1-1-111-111-1-1111-111-111-1
χ16111111111-1111111111-1-1-1-1-1-11-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ1722222-22220222222-2-2-200000020002-2-2-222222200000000000000000000-2-2-2-2222222000000000000000-2-2-2000000000
χ1822222-22220222222-2-2-200000020002-2-2-222-2-2-2-200000000000000000000-222-222-2-2-2-200000000000000022-2000000000
χ1922222-22220222222-2-2-200000020002-2-2-2-2-222-2-200000000000000000000-2-222-2-222-2-2000000000000000-222000000000
χ2022222-22220222222-2-2-200000020002-2-2-2-2-2-2-22200000000000000000000-22-22-2-2-2-2220000000000000002-22000000000
χ212222-12-12222-1-1-1-12-122222200-122-1-1-1-1222000022022-1-122-1-100002-1-1-1-1-1002-1-1000022-1-100-1-1-1-10020000-1-1-1000-1000
χ222222-12-12222-1-1-1-12-12222-2-200-122-1-1-1-12-2-200002-2022-1-1-2-21100002-1-1-1-1-100-21100002-2-1100-1-11100-200001-110001000
χ232222-12-12222-1-1-1-12-122-2-22200-122-1-1-1-12-2-20000-220-2-21122-1-100002-1-1-1-1-100-2110000-221-10011-1-100-2000011-10001000
χ242222-12-12222-1-1-1-12-122-2-2-2-200-122-1-1-1-12220000-2-20-2-211-2-21100002-1-1-1-1-1002-1-10000-2-2110011110020000-111000-1000
χ252222-12-122-22-1-1-1-12-122222200-1-2-21-1-1-12220000-2-2022-1-122-1-10000-21111-1002-1-10000-2-21100-1-1-1-100-20000-1110001000
χ262222-12-122-22-1-1-1-12-12222-2-200-1-2-21-1-1-12-2-20000-22022-1-1-2-2110000-21111-100-2110000-221-100-1-111002000011-1000-1000
χ272222-12-122-22-1-1-1-12-122-2-22200-1-2-21-1-1-12-2-200002-20-2-21122-1-10000-21111-100-21100002-2-110011-1-100200001-11000-1000
χ282222-12-122-22-1-1-1-12-122-2-2-2-200-1-2-21-1-1-12220000220-2-211-2-2110000-21111-1002-1-1000022-1-100111100-20000-1-1-10001000
χ29222-12222-12-12-12-1-122-1002222-12-12-12-1-10000220220000-1-12222-1-1-12-1-1-1-10200000-1-10-1022-100-1-1-1-10020-100-1-10000-10
χ30222-12222-12-12-12-1-122-10022-2-2-12-12-12-1-10000-2-202-20000-1-122-2-211-12-1-1-1-10-200000110-102-2100-1-11100-20100-11000010
χ31222-12222-12-12-12-1-122-100-2-222-12-12-12-1-10000-2-20-22000011-2-222-1-1-12-1-1-1-10-20000011010-22-10011-1-100-201001-1000010
χ32222-12222-12-12-12-1-122-100-2-2-2-2-12-12-12-1-10000220-2-2000011-2-2-2-211-12-1-1-1-10200000-1-1010-2-210011110020-100110000-10
χ33222-12222-1-2-12-12-1-122-1002222-1-21-2-12-1-10000220-2-20000-1-12222-1-11-2111-10200000-1-1010-2-2100-1-1-1-100-20-10011000010
χ34222-12222-1-2-12-12-1-122-10022-2-2-1-21-2-12-1-10000-2-20-220000-1-122-2-2111-2111-10-20000011010-22-100-1-11100201001-10000-10
χ35222-12222-1-2-12-12-1-122-100-2-222-1-21-2-12-1-10000-2-202-2000011-2-222-1-11-2111-10-200000110-102-210011-1-10020100-110000-10
χ36222-12222-1-2-12-12-1-122-100-2-2-2-2-1-21-2-12-1-1000022022000011-2-2-2-2111-2111-10200000-1-10-1022-100111100-20-100-1-1000010
χ3722-12222-122-1-12-12-12-12220022-1-122-1-12-1002200202-1-1220000-1-122-1-12-1-1-120000-1-100-1020-12-1-100-1-1020-100-10-1000-100
χ3822-12222-122-1-12-12-12-122200-2-2-1-122-1-12-100-2-20020-2-1-122000011-2-2-1-12-1-1-1-200001100-10201-2-1-100110-20100-101000100
χ3922-12222-122-1-12-12-12-12-2-20022-1-122-1-12-100-2-200-20211-2-20000-1-122-1-12-1-1-1-20000110010-20-121100-1-10-2010010-1000100
χ4022-12222-122-1-12-12-12-12-2-200-2-2-1-122-1-12-1002200-20-211-2-2000011-2-2-1-12-1-1-120000-1-10010-201-2110011020-100101000-100
χ4122-12222-12-2-1-12-12-12-12220022-11-2-2-1-12-1002200-20-2-1-1220000-1-12211-211-120000-1-10010-201-2-1-100-1-10-20-100101000100
χ4222-12222-12-2-1-12-12-12-122200-2-2-11-2-2-1-12-100-2-200-202-1-122000011-2-211-211-1-20000110010-20-12-1-1001102010010-1000-100
χ4322-12222-12-2-1-12-12-12-12-2-20022-11-2-2-1-12-100-2-20020-211-2-20000-1-12211-211-1-200001100-10201-21100-1-1020100-101000-100
χ4422-12222-12-2-1-12-12-12-12-2-200-2-2-11-2-2-1-12-100220020211-2-2000011-2-211-211-120000-1-100-1020-121100110-20-100-10-1000100
χ452-22220-2-2-20222-2-2-20002−22−2−i2i22000-20002-22i−2i2i−2i0002−22−22−22−2−i2i2−i2i20000000002-22i−2i2i−2i0000002−22−2−i2i2000000000−i2i20000
χ462-22220-2-2-20222-2-2-20002−22−2i2−i22000-20002-2−2i2i−2i2i0002−22−22−22−2i2−i2i2−i20000000002-2−2i2i−2i2i0000002−22−2i2−i2000000000i2−i20000
χ472-22220-2-2-20222-2-2-20002−2−22−i2i22000-2000-222i−2i−2i2i0002−22−2−22−22−i2i2−i2i2000000000-222i−2i−2i2i0000002−2−22−i2i2000000000i2−i20000
χ482-22220-2-2-20222-2-2-20002−2−22i2−i22000-2000-22−2i2i2i−2i0002−22−2−22−22i2−i2i2−i2000000000-22−2i2i2i−2i0000002−2−22i2−i2000000000−i2i20000
χ492-22220-2-2-20222-2-2-2000−222−2−i2i22000-2000-22−2i2i2i−2i000−22−222−22−2−i2i2−i2i2000000000-22−2i2i2i−2i000000−222−2−i2i2000000000i2−i20000
χ502-22220-2-2-20222-2-2-2000−222−2i2−i22000-2000-222i−2i−2i2i000−22−222−22−2i2−i2i2−i2000000000-222i−2i−2i2i000000−222−2i2−i2000000000−i2i20000
χ512-22220-2-2-20222-2-2-2000−22−22−i2i22000-20002-2−2i2i−2i2i000−22−22−22−22−i2i2−i2i20000000002-2−2i2i−2i2i000000−22−22−i2i2000000000−i2i20000
χ522-22220-2-2-20222-2-2-2000−22−22i2−i22000-20002-22i−2i2i−2i000−22−22−22−22i2−i2i2−i20000000002-22i−2i2i−2i000000−22−22i2−i2000000000i2−i20000
χ534444-2-4-24404-2-2-2-242-4-4000000-2000-222-444000000000000000000000000200-4-2-20000000000000000000002000000000
χ544444-2-4-24404-2-2-2-242-4-4000000-2000-222-4-4-4000000000000000000000000200422000000000000000000000-2000000000
χ55444-24-444-20-24-24-2-2-4-42000000-2000-2-4220000440000000000000000000020-400000-2-2000000000000000020000000000
χ56444-24-444-20-24-24-2-2-4-42000000-2000-2-4220000-4-40000000000000000000020400000220000000000000000-20000000000
χ57444-2-24-24-24-2-21-21-2-24-200440014-2-21-21-20000000400000-2-2-2-20000-2-211110000000000-20-200001100000000010000000
χ58444-2-24-24-24-2-21-21-2-24-200-4-40014-2-21-21-20000000-40000022220000-2-2111100000000002020000-1-1000000000-10000000
χ59444-2-24-24-2-4-2-21-21-2-24-20044001-4221-21-20000000-400000-2-2-2-2000022-1-1-110000000000202000011000000000-10000000
χ60444-2-24-24-2-4-2-21-21-2-24-200-4-4001-4221-21-200000004000002222000022-1-1-110000000000-20-20000-1-100000000010000000
χ6144-244-44-240-2-24-24-2-42-4000000-2000-22-42004400000000000000000000002-40000-2-200000000000000000200000000000
χ6244-244-44-240-2-24-24-2-42-4000000-2000-22-4200-4-400000000000000000000002400002200000000000000000-200000000000
χ6344-24-24-2-244-21-21-2-2-2-244400001-24-211-2-2000000400-2-2-2-200000000-21-2111000000000-20-2000110000000000100000000
χ6444-24-24-2-244-21-21-2-2-2-24-4-400001-24-211-2-2000000-400222200000000-21-2111000000000202000-1-10000000000-100000000
χ6544-24-24-2-24-4-21-21-2-2-2-2444000012-4211-2-2000000-400-2-2-2-2000000002-12-1-11000000000202000110000000000-100000000
χ6644-24-24-2-24-4-21-21-2-2-2-24-4-4000012-4211-2-20000004002222000000002-12-1-11000000000-20-2000-1-10000000000100000000
χ6744-2-2444-2-241-2-2-2-214-2-20000441-2-241-2-2100000000400000000-2-2-2-21-2-21110000000000000-2-2000011000000001000000
χ6844-2-2444-2-241-2-2-2-214-2-20000-4-41-2-241-2-2100000000-40000000022221-2-21110000000000000220000-1-100000000-1000000
χ6944-2-2444-2-2-41-2-2-2-214-2-2000044122-41-2-2100000000-400000000-2-2-2-2-122-1-1100000000000002200001100000000-1000000
χ7044-2-2444-2-2-41-2-2-2-214-2-20000-4-4122-41-2-21000000004000000002222-122-1-110000000000000-2-20000-1-1000000001000000
χ714-444-202-4-404-2-222-400022−2222−2200-200020004-4000000022−22−2222−22−220000000000000-220000000000−22−2200000000000000000
χ724-444-202-4-404-2-222-400022−22−222200-20002000-44000000022−22−22−22222−200000000000002-20000000000−222−200000000000000000
χ734-444-202-4-404-2-222-4000−222222−2200-20002000-440000000−22222−222−22−2200000000000002-200000000002−2−2200000000000000000
χ744-444-202-4-404-2-222-4000−2222−222200-200020004-40000000−22222−2−22222−20000000000000-2200000000002−22−200000000000000000
χ754-44-240-4-420-24-2-4220000022−22−2i22i2-2000200000004i−4i0000000−2222−22−2i22i2i2−i20000000000000−2i2i00000000−22i2−i2000000000000000
χ764-44-240-4-420-24-2-4220000022−222i2−2i2-200020000000−4i4i0000000−2222−222i2−2i2−i2i200000000000002i−2i00000000−22−i2i2000000000000000
χ774-44-240-4-420-24-2-42200000−2222−2i22i2-200020000000−4i4i00000002−2−2222−2i22i2i2−i200000000000002i−2i000000002−2i2−i2000000000000000
χ784-44-240-4-420-24-2-42200000−22222i2−2i2-2000200000004i−4i00000002−2−22222i2−2i2−i2i20000000000000−2i2i000000002−2−i2i2000000000000000
χ794-4-2440-42-40-2-242-4200022−2200−2i22i2-20002000004i−4i00000−2222−220000i2−i2−2i22i200000000000−2i2i00000000−2200i2−i2000000000000000
χ804-4-2440-42-40-2-242-4200022−22002i2−2i2-2000200000−4i4i00000−2222−220000−i2i22i2−2i2000000000002i−2i00000000−2200−i2i2000000000000000
χ814-4-2440-42-40-2-242-42000−222200−2i22i2-2000200000−4i4i000002−2−22220000i2−i2−2i22i2000000000002i−2i000000002−200i2−i2000000000000000
χ824-4-2440-42-40-2-242-42000−2222002i2−2i2-20002000004i−4i000002−2−22220000−i2i22i2−2i200000000000−2i2i000000002−200−i2i2000000000000000
χ83888-4-4-8-48-40-4-42-42-44-84000000200024-2400000000000000000000000000-2000000000000000000000000000000000000
χ8488-48-4-8-4-480-42-42-4-444-800000020002-24400000000000000000000000000-2000000000000000000000000000000000000
χ8588-4-48-88-4-402-4-4-4-42-8440000002000244-200000000000000000000000000-2000000000000000000000000000000000000
χ8688-4-4-48-4-4-48222222-4-4-4000000-1-4-4-4-1222000000000000000000000222-1-1-1000000000000000000000000000000000000
χ8788-4-4-48-4-4-4-8222222-4-4-4000000-1444-1222000000000000000000000-2-2-211-1000000000000000000000000000000000000
χ8888-4-4-4-8-4-4-40222222444000000-1000-1-2-2-2000000000000000000000000−3i33i31000000000000000000000000000000000000
χ8988-4-4-4-8-4-4-40222222444000000-1000-1-2-2-20000000000000000000000003i3−3i31000000000000000000000000000000000000
χ908-88-4-404-840-4-424-240000042−42002000-20000000000000000−2222−22220000000000000000000000000002−200000000000000000
χ918-88-4-404-840-4-424-2400000−4242002000-2000000000000000022−2222−22000000000000000000000000000−2200000000000000000
χ928-8-48-4044-80-42-4-24400042−4200002000-2000000000000−2222−2222000000000000000000000000000002−20000000000000000000
χ938-8-48-4044-80-42-4-244000−424200002000-200000000000022−2222−2200000000000000000000000000000−220000000000000000000
χ948-8-4-480-84402-4-444-20000000−4i24i22000-2000000000000000000002i2−2i22i2−2i20000000000000000000000000−i2i2000000000000000
χ958-8-4-480-84402-4-444-200000004i2−4i22000-200000000000000000000−2i22i2−2i22i20000000000000000000000000i2−i2000000000000000
χ9616-16-8-8-808880444-4-4-4000000000-20002000000000000000000000000000000000000000000000000000000000000000000

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