Finite Group Databasebeta

← Group #13171675

Character table — Group #13171675

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1122222224444444444666666888888889999991212121212121212121212121212121616161616161818181818181818182424242424242424242424243636363636364848485454727272108
order123334666333466612121288888836121212121212224444224242424242424242424242424121212121212224661212121266661212242424242424224661266128866124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-11111111111-1-1-1-111-111111111-1-1-1-1111111-1-1111-1-1-1-11111-1-11111-1-1-1-11-1-1111-1-1-1-1-11-1
χ3111111111111111111111-1-11111111111-1-111-1-11-111111-1-1-1-111111111111-1-1-1-111-1-11-11-11111-1-1111-1-11-1-11-11-1-11-1-1-1
χ4111111111111111111111-1-1-1-111111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1111111-11-1-1-1-1-1111-11-1-1-111-1-1-1-1-11-1-11-11-1-111-11-11
χ51111111111111111111-1-1111111111111-1-1-1-111-111-1-1-1-111111111111111-11-1-1-1-1-111-11-1111-1-11111-11-1-11-1-111-1-1-11-1-1
χ61111111111111111111-1-111-1-111111111-1-111-1-1-11-1-1-1-1-11111-1-1-1-11111111-1-1-1-111-1-1-11-11-1-1-1-111-1-11-1-11-1-1-11-1111-1-11
χ71111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-111-1-11-1-11-1-1111-1-111
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
χ9111111111111-111111111111111-1-1-1111111111-1-1-1111111111111-1-1-11-1-1111111111-1-1-1-1-1-1111111-1-1-1111-1-1-111-1-1-1-1
χ10111111111111-11111111111-1-111-1-1-111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-111-1-1-11-1-11-1-111-11
χ11111111111111-111111111-1-11111-1-1-1111-1-111-1-1-11-11111-1-1-1-11111-1-1-11-1-11-1-1-1-111-1-1-11-11-1-111-1-111-1111-1-1-11-1-1-1-1111
χ12111111111111-111111111-1-1-1-111-1-1-1111-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-111-11-111111-1-1-1-11-11-11-1-111111-11-1
χ13111111111111-1111111-1-1111111-1-1-1111-1-1-1-1111-1-1-1-1-1-111111111-1-1-11-1-1-11-1-1-1-1-1111-11-1-1-1-1-111111-11-11-11-1-1-1-11-111
χ14111111111111-1111111-1-111-1-111-1-1-1111-1-111-1-11-11-1-1-1-11111-1-1-1-1-1-1-11-1-11-1-1-1-111-1-11-11-111-1-111-1-1-1111-1-11-1111-111-1
χ15111111111111-1111111-1-1-1-11111-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-1111-1-1-1-11111-1-1-1-1-1-11111-1-1-1111-11111-1-1
χ16111111111111-1111111-1-1-1-1-1-111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ1722222-22222220222-2-2-200000022000-2-2-2222222000000000000000000-200-2-2-2222222000000000000000-2-2-2000000000
χ1822222-22222220222-2-2-200000022000-2-2-222-2-2-2-2000000000000000000-20022-222-2-2-2-200000000000000022-2000000000
χ1922222-22222220222-2-2-200000022000-2-2-2-2-222-2-2000000000000000000-200-222-2-222-2-2000000000000000-222000000000
χ2022222-22222220222-2-2-200000022000-2-2-2-2-2-2-222000000000000000000-2002-22-2-2-2-2220000000000000002-22000000000
χ212222-122-12-12-122-1-12-12002222-1-12-122-1-1000022022000022-1-122-1-12-1-1-1-1-10200000-1-1020-12-100-1-1-1-10200-100-1-1000-100
χ222222-122-12-12-122-1-12-120022-2-2-1-12-122-1-10000-2-202-2000022-1-1-2-2112-1-1-1-1-10-20000011020-1-2100-1-1110-200100-11000100
χ232222-122-12-12-122-1-12-1200-2-222-1-12-122-1-10000-2-20-220000-2-21122-1-12-1-1-1-1-10-200000110-2012-10011-1-10-2001001-1000100
χ242222-122-12-12-122-1-12-1200-2-2-2-2-1-12-122-1-10000220-2-20000-2-211-2-2112-1-1-1-1-10200000-1-10-201-210011110200-10011000-100
χ252222-122-12-12-1-22-1-12-12002222-1-1-21-22-1-10000220-2-2000022-1-122-1-1-211-1110200000-1-10-201-2100-1-1-1-10-200-10011000100
χ262222-122-12-12-1-22-1-12-120022-2-2-1-1-21-22-1-10000-2-20-22000022-1-1-2-211-211-1110-200000110-2012-100-1-11102001001-1000-100
χ272222-122-12-12-1-22-1-12-1200-2-222-1-1-21-22-1-10000-2-202-20000-2-21122-1-1-211-1110-20000011020-1-210011-1-10200100-11000-100
χ282222-122-12-12-1-22-1-12-1200-2-2-2-2-1-1-21-22-1-10000220220000-2-211-2-211-211-1110200000-1-1020-12-10011110-200-100-1-1000100
χ29222-122-122-1-122-12-1-122220022-1-1-122-12-100220020222-1-10000-1-122-12-1-1-1-120000-1-10020-10-12-1-100-1-1200-100-10-100-1000
χ30222-122-122-1-122-12-1-1222200-2-2-1-1-122-12-100-2-20020-222-1-1000011-2-2-12-1-1-1-1-20000110020-101-2-1-10011-200100-101001000
χ31222-122-122-1-122-12-1-122-2-20022-1-1-122-12-100-2-200-202-2-2110000-1-122-12-1-1-1-1-200001100-2010-121100-1-1-20010010-1001000
χ32222-122-122-1-122-12-1-122-2-200-2-2-1-1-122-12-1002200-20-2-2-211000011-2-2-12-1-1-1-120000-1-100-20101-2110011200-10010100-1000
χ33222-122-122-1-12-2-12-1-122220022-1-11-2-2-12-1002200-20-222-1-10000-1-1221-21-11120000-1-100-20101-2-1-100-1-1-200-100101001000
χ34222-122-122-1-12-2-12-1-1222200-2-2-1-11-2-2-12-100-2-200-20222-1-1000011-2-21-21-111-200001100-2010-12-1-1001120010010-100-1000
χ35222-122-122-1-12-2-12-1-122-2-20022-1-11-2-2-12-100-2-20020-2-2-2110000-1-1221-21-111-20000110020-101-21100-1-1200100-10100-1000
χ36222-122-122-1-12-2-12-1-122-2-200-2-2-1-11-2-2-12-1002200202-2-211000011-2-21-21-11120000-1-10020-10-12110011-200-100-10-1001000
χ3722-122222-12-1-12-1-1222-1222200-1-122-1-1-12220000220-1-122-1-1220000-1-12-1-1-1002-1-10000-1-12200-1-1-1-10000200-1-1-100000-10
χ3822-122222-12-1-12-1-1222-122-2-200-1-122-1-1-12-2-200002-20-1-12211-2-20000-1-12-1-1-100-2110000-112-200-1-1110000-2001-110000010
χ3922-122222-12-1-12-1-1222-1-2-22200-1-122-1-1-12-2-20000-22011-2-2-1-1220000-1-12-1-1-100-21100001-1-220011-1-10000-20011-10000010
χ4022-122222-12-1-12-1-1222-1-2-2-2-200-1-122-1-1-12220000-2-2011-2-211-2-20000-1-12-1-1-1002-1-1000011-2-20011110000200-11100000-10
χ4122-122222-12-1-1-2-1-1222-1222200-1-1-2-21-1-12220000-2-20-1-122-1-122000011-2-111002-1-1000011-2-200-1-1-1-10000-200-1110000010
χ4222-122222-12-1-1-2-1-1222-122-2-200-1-1-2-21-1-12-2-20000-220-1-12211-2-2000011-2-11100-21100001-1-2200-1-111000020011-100000-10
χ4322-122222-12-1-1-2-1-1222-1-2-22200-1-1-2-21-1-12-2-200002-2011-2-2-1-122000011-2-11100-2110000-112-20011-1-100002001-1100000-10
χ4422-122222-12-1-1-2-1-1222-1-2-2-2-200-1-1-2-21-1-1222000022011-2-211-2-2000011-2-111002-1-10000-1-1220011110000-200-1-1-10000010
χ452-22220-2-2-22220-2-2-2000−i2i2−i2i22−22-20000002-22i−2i2i−2i000−i2i2−i2i2−i2i2−i2i22−22−20000000002-22i−2i2i−2i000000−i2i2−i2i22−20000000002−20000
χ462-22220-2-2-22220-2-2-2000−i2i2−i2i2−222-20000002-2−2i2i−2i2i000−i2i2−i2i2−i2i2−i2i2−22−220000000002-2−2i2i−2i2i000000−i2i2−i2i2−22000000000−220000
χ472-22220-2-2-22220-2-2-2000−i2i2i2−i22−22-2000000-222i−2i−2i2i000−i2i2−i2i2i2−i2i2−i22−22−2000000000-222i−2i−2i2i000000−i2i2i2−i22−2000000000−220000
χ482-22220-2-2-22220-2-2-2000−i2i2i2−i2−222-2000000-22−2i2i2i−2i000−i2i2−i2i2i2−i2i2−i2−22−22000000000-22−2i2i2i−2i000000−i2i2i2−i2−220000000002−20000
χ492-22220-2-2-22220-2-2-2000i2−i2−i2i22−22-2000000-22−2i2i2i−2i000i2−i2i2−i2−i2i2−i2i22−22−2000000000-22−2i2i2i−2i000000i2−i2−i2i22−2000000000−220000
χ502-22220-2-2-22220-2-2-2000i2−i2−i2i2−222-2000000-222i−2i−2i2i000i2−i2i2−i2−i2i2−i2i2−22−22000000000-222i−2i−2i2i000000i2−i2−i2i2−220000000002−20000
χ512-22220-2-2-22220-2-2-2000i2−i2i2−i22−22-20000002-2−2i2i−2i2i000i2−i2i2−i2i2−i2i2−i22−22−20000000002-2−2i2i−2i2i000000i2−i2i2−i22−20000000002−20000
χ522-22220-2-2-22220-2-2-2000i2−i2i2−i2−222-20000002-22i−2i2i−2i000i2−i2i2−i2i2−i2i2−i2−22−220000000002-22i−2i2i−2i000000i2−i2i2−i2−22000000000−220000
χ534444-2-44-24-24-204-2-2-42-4000000-2-2000-4220000440000000000000000002000-400000-2-2000000000000000020000000000
χ544444-2-44-24-24-204-2-2-42-4000000-2-2000-4220000-4-40000000000000000002000400000220000000000000000-20000000000
χ55444-24-4-244-2-240-24-22-4-4000000-2-20002-42004400000000000000000000200-40000-2-200000000000000000200000000000
χ56444-24-4-244-2-240-24-22-4-4000000-2-20002-4200-4-400000000000000000000200400002200000000000000000-200000000000
χ57444-2-24-2-241-2-24-2-21-2-2400004411-2-24-2-2100000000400000000-2-2-2-2-2-211110000000000000-2-2000011000000001000000
χ58444-2-24-2-241-2-24-2-21-2-240000-4-411-2-24-2-2100000000-4000000002222-2-211110000000000000220000-1-100000000-1000000
χ59444-2-24-2-241-2-2-4-2-21-2-240000441122-4-2-2100000000-400000000-2-2-2-222-11-1-100000000000002200001100000000-1000000
χ60444-2-24-2-241-2-2-4-2-21-2-240000-4-41122-4-2-2100000000400000000222222-11-1-10000000000000-2-20000-1-1000000001000000
χ6144-244-444-24-2-20-2-24-4-42000000-2-200022-444000000000000000000000020000-4-2-20000000000000000000002000000000
χ6244-244-444-24-2-20-2-24-4-42000000-2-200022-4-4-4000000000000000000000020000422000000000000000000000-2000000000
χ6344-24-244-2-2-2-214-21-24-2-2004400114-2-2-21-20000000400000-2-2-2-20000-21-21110000000000-20-200001100000000010000000
χ6444-24-244-2-2-2-214-21-24-2-200-4-400114-2-2-21-20000000-40000022220000-21-211100000000002020000-1-1000000000-10000000
χ6544-24-244-2-2-2-21-4-21-24-2-200440011-422-21-20000000-400000-2-2-2-200002-121-1-10000000000202000011000000000-10000000
χ6644-24-244-2-2-2-21-4-21-24-2-200-4-40011-422-21-20000000400000222200002-121-1-10000000000-20-20000-1-100000000010000000
χ6744-2-244-24-2-21-241-2-2-24-244000011-24-21-2-2000000400-2-2-2-2000000001-2-2111000000000-20-2000110000000000100000000
χ6844-2-244-24-2-21-241-2-2-24-2-4-4000011-24-21-2-2000000-4002222000000001-2-2111000000000202000-1-10000000000-100000000
χ6944-2-244-24-2-21-2-41-2-2-24-2440000112-421-2-2000000-400-2-2-2-200000000-1221-1-1000000000202000110000000000-100000000
χ7044-2-244-24-2-21-2-41-2-2-24-2-4-40000112-421-2-2000000400222200000000-1221-1-1000000000-20-2000-1-10000000000100000000
χ714-444-20-42-4-24-20-42200000−2i22i222−22-2200000000004i−4i0000000−2i22i2i2−i222−22−220000000000000−2i2i00000000i2−i2−22000000000000000
χ724-444-20-42-4-24-20-42200000−2i22i2−2222-220000000000−4i4i0000000−2i22i2i2−i2−22222−200000000000002i−2i00000000i2−i22−2000000000000000
χ734-444-20-42-4-24-20-422000002i2−2i222−22-220000000000−4i4i00000002i2−2i2−i2i222−22−2200000000000002i−2i00000000−i2i2−22000000000000000
χ744-444-20-42-4-24-20-422000002i2−2i2−2222-2200000000004i−4i00000002i2−2i2−i2i2−22222−20000000000000−2i2i00000000−i2i22−2000000000000000
χ754-44-2402-4-4-2-2402-42000−2i22i20022−22-22000000004i−4i00000−2i22i2i2−i20000−2222−2200000000000−2i2i00000000i2−i200−22000000000000000
χ764-44-2402-4-4-2-2402-42000−2i22i200−2222-2200000000−4i4i00000−2i22i2i2−i200002−2−2222000000000002i−2i00000000i2−i2002−2000000000000000
χ774-44-2402-4-4-2-2402-420002i2−2i20022−22-2200000000−4i4i000002i2−2i2−i2i20000−2222−22000000000002i−2i00000000−i2i200−22000000000000000
χ784-44-2402-4-4-2-2402-420002i2−2i200−2222-22000000004i−4i000002i2−2i2−i2i200002−2−222200000000000−2i2i00000000−i2i2002−2000000000000000
χ794-4-2440-4-424-2-2022-4000−2i22i2−2i22i200-220000004-40000000i2−i2−2i22i2i2−i2−2i22i20000000000000-220000000000i2−i2i2−i200000000000000000
χ804-4-2440-4-424-2-2022-4000−2i22i22i2−2i200-22000000-440000000i2−i2−2i22i2−i2i22i2−2i200000000000002-20000000000i2−i2−i2i200000000000000000
χ814-4-2440-4-424-2-2022-40002i2−2i2−2i22i200-22000000-440000000−i2i22i2−2i2i2−i2−2i22i200000000000002-20000000000−i2i2i2−i200000000000000000
χ824-4-2440-4-424-2-2022-40002i2−2i22i2−2i200-220000004-40000000−i2i22i2−2i2−i2i22i2−2i20000000000000-220000000000−i2i2−i2i200000000000000000
χ83888-4-4-8-4-482-4-40-4-4244-80000002200044-2000000000000000000000000-200000000000000000000000000000000000000
χ8488-48-4-88-4-4-4-420-42-4-844000000220004-24000000000000000000000000-200000000000000000000000000000000000000
χ8588-4-48-8-48-4-42-402-4-44-8400000022000-244000000000000000000000000-200000000000000000000000000000000000000
χ8688-4-4-48-4-4-42228222-4-4-4000000-1-1-4-4-4222000000000000000000000222-1-1-1000000000000000000000000000000000000
χ8788-4-4-48-4-4-4222-8222-4-4-4000000-1-1444222000000000000000000000-2-2-2-111000000000000000000000000000000000000
χ8888-4-4-4-8-4-4-42220222444000000-1-1000-2-2-20000000000000000000000001−3i33i3000000000000000000000000000000000000
χ8988-4-4-4-8-4-4-42220222444000000-1-1000-2-2-200000000000000000000000013i3−3i3000000000000000000000000000000000000
χ908-88-4-4044-82-4-4044-2000000042−422-200000000000000000000000−2222−222200000000000000000000000002−2000000000000000
χ918-88-4-4044-82-4-4044-20000000−42422-20000000000000000000000022−2222−220000000000000000000000000−22000000000000000
χ928-8-48-40-844-4-4204-2400000−4i24i2002-200000000000000000002i2−2i22i2−2i2000000000000000000000000000−i2i200000000000000000
χ938-8-48-40-844-4-4204-24000004i2−4i2002-20000000000000000000−2i22i2−2i22i2000000000000000000000000000i2−i200000000000000000
χ948-8-4-4804-84-42-40-244000−4i24i200002-20000000000000002i2−2i22i2−2i200000000000000000000000000000−i2i20000000000000000000
χ958-8-4-4804-84-42-40-2440004i2−4i200002-2000000000000000−2i22i2−2i22i200000000000000000000000000000i2−i20000000000000000000
χ9616-16-8-8-808884440-4-4-4000000000-22000000000000000000000000000000000000000000000000000000000000000000000

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