Finite Group Databasebeta

← Group #13171578

Character table — Group #13171578

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1122222224444444444666666888888889999991212121212121212121212121212121616161616161818181818181818182424242424242424242424243636363636364848485454727272108
order12333466623336661212128888883666612121222444424424242424242424242424242466666122246612121212661212121224242424242424466126121288612122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-11111111111-1-1-1-1-11111111111-1-1-1-1111111-1-1111-1-1-1-1-1-111111111-1-11-1-1-1-11-111-1-11-1-1-1
χ3111111111111111111111-1-11111111111-1-111-1-111-11111-1-1-1-111111111111-1-1-1-111-1-1111-11-111-1-111-11-11-1-111-1-1-1-11-1-1
χ4111111111111111111111-1-1-1-111111111-1-1-1-111-11-11111-1-1-1-1-1-1-1-1111111-11-1-1-1-1-111-1-11-11-111-1-1-1-1-1-11-11-1-11-111-1-111
χ51111111111111111111-1-1111111111111-1-1-1-1111-11-1-1-1-111111111111111-11-1-1-1-1-11111-11-11-1-11111-1-11-11-11-11-1-1-1-11-1
χ61111111111111111111-1-111-1-111111111-1-111-1-1-1-11-1-1-1-11111-1-1-1-11111111-1-1-1-111-1-1-1-1-11-11-1-111-1-1-11-11-1-1-1-1111-11-11
χ71111111111111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1111-1-11
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
χ10111111111-11111111111111-1-11-1-1-1111111-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-1-1-11111-1-1-111-1-111-1-1-1-1-1111
χ11111111111-111111111111-1-1111-1-1-11111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1-111-1-1-1-111-1-1-1-1-11-1111-1-1111-111-1-1-1-11-1-11-111
χ12111111111-111111111111-1-1-1-11-1-1-11111-1-1-1-1111-111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11111-11-1111-1-1-1-111-1-11-11-111111-1-1
χ13111111111-1111111111-1-111111-1-1-11111-1-1-1-111-11-1-1-1-1-111111111-1-1-1-1-11-11-1-1-1-1-111-1-11-11-1-1-1111111-1-11-1-11-1-1-111-11
χ14111111111-1111111111-1-111-1-11-1-1-11111-1-111-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111-11-1-1-111-1-11-111-1-111-1111-11-1
χ15111111111-1111111111-1-1-1-1111-1-1-1111111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1111-1-1-1-1-1-11111-1-1-1-111-111-1-11-11111-111-1
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
χ212222-12-1222-1-122-1-1-122222200-122-1-12-1-122000002222-1-122-1-10000-1-12-1-1-1002-1-1000000-1-122-1-1-1-10020000-10-1-100-1000
χ222222-12-1222-1-122-1-1-12222-2-200-122-1-12-1-1-2-2000002-222-1-1-2-2110000-1-12-1-1-100-211000000-112-2-1-11100-2000010-11001000
χ232222-12-1222-1-122-1-1-122-2-22200-122-1-12-1-1-2-200000-22-2-21122-1-10000-1-12-1-1-100-2110000001-1-2211-1-100-20000101-1001000
χ242222-12-1222-1-122-1-1-122-2-2-2-200-122-1-12-1-12200000-2-2-2-211-2-2110000-1-12-1-1-1002-1-100000011-2-211110020000-101100-1000
χ252222-12-122-2-1-122-1-1-122222200-1-2-21-12-1-12200000-2-222-1-122-1-1000011-211-1002-1-100000011-2-2-1-1-1-100-20000-1011001000
χ262222-12-122-2-1-122-1-1-12222-2-200-1-2-21-12-1-1-2-200000-2222-1-1-2-211000011-211-100-2110000001-1-22-1-1110020000101-100-1000
χ272222-12-122-2-1-122-1-1-122-2-22200-1-2-21-12-1-1-2-2000002-2-2-21122-1-1000011-211-100-211000000-112-211-1-1002000010-1100-1000
χ282222-12-122-2-1-122-1-1-122-2-2-2-200-1-2-21-12-1-1220000022-2-211-2-211000011-211-1002-1-1000000-1-122111100-20000-10-1-1001000
χ29222-12222-122-1-1-12-122-1002222-12-12-1-12-10000222020000-1-12222-1-12-1-1-1-1-10200000-1-12-1020-100-1-1-1-10020-10-10-10000-10
χ30222-12222-122-1-1-12-122-10022-2-2-12-12-1-12-10000-2-2-2020000-1-122-2-2112-1-1-1-1-10-20000011-21020-100-1-11100-201010-1000010
χ31222-12222-122-1-1-12-122-100-2-222-12-12-1-12-10000-2-220-2000011-2-222-1-12-1-1-1-1-10-200000112-10-2010011-1-100-2010-101000010
χ32222-12222-122-1-1-12-122-100-2-2-2-2-12-12-1-12-1000022-20-2000011-2-2-2-2112-1-1-1-1-10200000-1-1-210-2010011110020-101010000-10
χ33222-12222-1-22-1-1-12-122-1002222-1-21-2-1-12-1000022-20-20000-1-12222-1-1-21111-10200000-1-1-210-20100-1-1-1-100-20-10101000010
χ34222-12222-1-22-1-1-12-122-10022-2-2-1-21-2-1-12-10000-2-220-20000-1-122-2-211-21111-10-200000112-10-20100-1-111002010-1010000-10
χ35222-12222-1-22-1-1-12-122-100-2-222-1-21-2-1-12-10000-2-2-202000011-2-222-1-1-21111-10-20000011-21020-10011-1-100201010-10000-10
χ36222-12222-1-22-1-1-12-122-100-2-2-2-2-1-21-2-1-12-1000022202000011-2-2-2-211-21111-10200000-1-12-1020-100111100-20-10-10-1000010
χ3722-12222-122-12-1-1-122-12220022-1-122-1-1-12002200220-1-1220000-1-122-12-1-1-1-120000-1-100-1220-10-1-100-1-1020-100-1-10000-100
χ3822-12222-122-12-1-1-122-122200-2-2-1-122-1-1-1200-2-200-220-1-122000011-2-2-12-1-1-1-1-2000011001-220-10-1-100110-201001-10000100
χ3922-12222-122-12-1-1-122-12-2-20022-1-122-1-1-1200-2-2002-2011-2-20000-1-122-12-1-1-1-1-200001100-12-20101100-1-10-20100-110000100
χ4022-12222-122-12-1-1-122-12-2-200-2-2-1-122-1-1-12002200-2-2011-2-2000011-2-2-12-1-1-1-120000-1-1001-2-2010110011020-100110000-100
χ4122-12222-12-2-12-1-1-122-12220022-11-2-2-1-1-12002200-2-20-1-1220000-1-1221-2111-120000-1-1001-2-2010-1-100-1-10-20-100110000100
χ4222-12222-12-2-12-1-1-122-122200-2-2-11-2-2-1-1-1200-2-2002-20-1-122000011-2-21-2111-1-200001100-12-2010-1-10011020100-110000-100
χ4322-12222-12-2-12-1-1-122-12-2-20022-11-2-2-1-1-1200-2-200-22011-2-20000-1-1221-2111-1-2000011001-220-101100-1-10201001-10000-100
χ4422-12222-12-2-12-1-1-122-12-2-200-2-2-11-2-2-1-1-1200220022011-2-2000011-2-21-2111-120000-1-100-1220-101100110-20-100-1-10000100
χ452-22220-2-2-20222-2-2-2000−i2i2−i2i22−22000-20002-22i−2i2i−2i000−i2i2−i2i2−i2i2−i2i22−22−20000000002-22i−2i2i−2i000000−i2i2−i2i22−20000000002−20000
χ462-22220-2-2-20222-2-2-2000−i2i2−i2i2−222000-20002-2−2i2i−2i2i000−i2i2−i2i2−i2i2−i2i2−22−220000000002-2−2i2i−2i2i000000−i2i2−i2i2−22000000000−220000
χ472-22220-2-2-20222-2-2-2000−i2i2i2−i22−22000-2000-222i−2i−2i2i000−i2i2−i2i2i2−i2i2−i22−22−2000000000-222i−2i−2i2i000000−i2i2i2−i22−2000000000−220000
χ482-22220-2-2-20222-2-2-2000−i2i2i2−i2−222000-2000-22−2i2i2i−2i000−i2i2−i2i2i2−i2i2−i2−22−22000000000-22−2i2i2i−2i000000−i2i2i2−i2−220000000002−20000
χ492-22220-2-2-20222-2-2-2000i2−i2−i2i22−22000-2000-22−2i2i2i−2i000i2−i2i2−i2−i2i2−i2i22−22−2000000000-22−2i2i2i−2i000000i2−i2−i2i22−2000000000−220000
χ502-22220-2-2-20222-2-2-2000i2−i2−i2i2−222000-2000-222i−2i−2i2i000i2−i2i2−i2−i2i2−i2i2−22−22000000000-222i−2i−2i2i000000i2−i2−i2i2−220000000002−20000
χ512-22220-2-2-20222-2-2-2000i2−i2i2−i22−22000-20002-2−2i2i−2i2i000i2−i2i2−i2i2−i2i2−i22−22−20000000002-2−2i2i−2i2i000000i2−i2i2−i22−20000000002−20000
χ522-22220-2-2-20222-2-2-2000i2−i2i2−i2−222000-20002-22i−2i2i−2i000i2−i2i2−i2i2−i2i2−i2−22−220000000002-22i−2i2i−2i000000i2−i2i2−i2−22000000000−220000
χ534444-2-4-2440-2-244-2-22-4-4000000-2000-2-42244000000000000000000000000200-4-2-20000000000000000000002000000000
χ544444-2-4-2440-2-244-2-22-4-4000000-2000-2-422-4-4000000000000000000000000200422000000000000000000000-2000000000
χ55444-24-444-204-2-2-24-2-4-42000000-2000-22-420000440000000000000000000020-400000-2-2000000000000000020000000000
χ56444-24-444-204-2-2-24-2-4-42000000-2000-22-420000-4-40000000000000000000020400000220000000000000000-20000000000
χ57444-2-24-24-24-21-2-2-21-24-200440014-2-21-2-210000000040000-2-2-2-20000-21-2111000000000000-20-2001100000000001000000
χ58444-2-24-24-24-21-2-2-21-24-200-4-40014-2-21-2-2100000000-4000022220000-21-211100000000000020200-1-10000000000-1000000
χ59444-2-24-24-2-4-21-2-2-21-24-20044001-4221-2-2100000000-40000-2-2-2-200002-12-1-1100000000000020200110000000000-1000000
χ60444-2-24-24-2-4-21-2-2-21-24-200-4-4001-4221-2-210000000040000222200002-12-1-11000000000000-20-200-1-100000000001000000
χ6144-244-44-240-24-2-2-24-42-4000000-2000-222-4004400000000000000000000002-40000-2-200000000000000000200000000000
χ6244-244-44-240-24-2-2-24-42-4000000-2000-222-400-4-400000000000000000000002400002200000000000000000-200000000000
χ6344-24-24-2-2441-2-2-21-2-2-244400001-24-21-21-2000000040-2-2-2-2000000001-2-211100000000000-20-20110000000000010000000
χ6444-24-24-2-2441-2-2-21-2-2-24-4-400001-24-21-21-20000000-402222000000001-2-2111000000000002020-1-100000000000-10000000
χ6544-24-24-2-24-41-2-2-21-2-2-2444000012-421-21-20000000-40-2-2-2-200000000-122-1-110000000000020201100000000000-10000000
χ6644-24-24-2-24-41-2-2-21-2-2-24-4-4000012-421-21-2000000040222200000000-122-1-1100000000000-20-20-1-10000000000010000000
χ6744-2-2444-2-24-2-211-2-24-2-20000441-2-2411-2-200000040000000000-2-2-2-2-2-21111000000000-2-20000000011000000100000000
χ6844-2-2444-2-24-2-211-2-24-2-20000-4-41-2-2411-2-2000000-400000000002222-2-211110000000002200000000-1-1000000-100000000
χ6944-2-2444-2-2-4-2-211-2-24-2-2000044122-411-2-2000000-40000000000-2-2-2-222-1-1-11000000000220000000011000000-100000000
χ7044-2-2444-2-2-4-2-211-2-24-2-20000-4-4122-411-2-200000040000000000222222-1-1-11000000000-2-200000000-1-1000000100000000
χ714-444-202-4-40-2-24-422000−2i22i2−2i22i200-200020004-40000000−2i22i2i2−i2−2i22i2i2−i20000000000000-220000000000i2−i2i2−i200000000000000000
χ724-444-202-4-40-2-24-422000−2i22i22i2−2i200-20002000-440000000−2i22i2i2−i22i2−2i2−i2i200000000000002-20000000000i2−i2−i2i200000000000000000
χ734-444-202-4-40-2-24-4220002i2−2i2−2i22i200-20002000-4400000002i2−2i2−i2i2−2i22i2i2−i200000000000002-20000000000−i2i2i2−i200000000000000000
χ744-444-202-4-40-2-24-4220002i2−2i22i2−2i200-200020004-400000002i2−2i2−i2i22i2−2i2−i2i20000000000000-220000000000−i2i2−i2i200000000000000000
χ754-44-240-4-4204-2-22-4200000−2i22i222−22-2000200000004i−4i0000000i2−i2−2i22i222−22−220000000000000−2i2i00000000i2−i2−22000000000000000
χ764-44-240-4-4204-2-22-4200000−2i22i2−2222-200020000000−4i4i0000000i2−i2−2i22i2−22222−200000000000002i−2i00000000i2−i22−2000000000000000
χ774-44-240-4-4204-2-22-42000002i2−2i222−22-200020000000−4i4i0000000−i2i22i2−2i222−22−2200000000000002i−2i00000000−i2i2−22000000000000000
χ784-44-240-4-4204-2-22-42000002i2−2i2−2222-2000200000004i−4i0000000−i2i22i2−2i2−22222−20000000000000−2i2i00000000−i2i22−2000000000000000
χ794-4-2440-42-40-24-222-4000−2i22i20022−22-20002000004i−4i00000i2−i2−2i22i20000−2222−2200000000000−2i2i00000000i2−i200−22000000000000000
χ804-4-2440-42-40-24-222-4000−2i22i200−2222-2000200000−4i4i00000i2−i2−2i22i200002−2−2222000000000002i−2i00000000i2−i2002−2000000000000000
χ814-4-2440-42-40-24-222-40002i2−2i20022−22-2000200000−4i4i00000−i2i22i2−2i20000−2222−22000000000002i−2i00000000−i2i200−22000000000000000
χ824-4-2440-42-40-24-222-40002i2−2i200−2222-20002000004i−4i00000−i2i22i2−2i200002−2−222200000000000−2i2i00000000−i2i2002−2000000000000000
χ83888-4-4-8-48-40-42-4-4-424-840000002000244-200000000000000000000000000-2000000000000000000000000000000000000
χ8488-48-4-8-4-4802-4-4-42-444-8000000200024-2400000000000000000000000000-2000000000000000000000000000000000000
χ8588-4-48-88-4-40-4-422-4-4-84400000020002-24400000000000000000000000000-2000000000000000000000000000000000000
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
χ908-88-4-404-840-42-444-200000−4i24i2002000-200000000000000002i2−2i22i2−2i2000000000000000000000000000−i2i200000000000000000
χ918-88-4-404-840-42-444-2000004i2−4i2002000-20000000000000000−2i22i2−2i22i2000000000000000000000000000i2−i200000000000000000
χ928-8-48-4044-802-4-44-24000−4i24i200002000-20000000000002i2−2i22i2−2i200000000000000000000000000000−i2i20000000000000000000
χ938-8-48-4044-802-4-44-240004i2−4i200002000-2000000000000−2i22i2−2i22i200000000000000000000000000000i2−i20000000000000000000
χ948-8-4-480-8440-4-42-244000000042−422000-200000000000000000000−2222−222200000000000000000000000002−2000000000000000
χ958-8-4-480-8440-4-42-2440000000−42422000-20000000000000000000022−2222−220000000000000000000000000−22000000000000000
χ9616-16-8-8-808880444-4-4-4000000000-20002000000000000000000000000000000000000000000000000000000000000000000

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