Finite Group Databasebeta

← Group #13180504

Character table — Group #13180504

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112223344444688888899121212121212121216161818181818181824242424242424242424272736363636363636363648484848545454545472727272
order1234644336612233661212222244121212121212466888866666612121212442244122424242466121228888661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-1111111111-1-1-1-1111111-1-1-1-111-1-1111-1-1-1-111-1-11-1-1-1-1-1-111
χ3111111111111111111111-1-111111111111-1-1-1-1-1-11-1-1111111111-1-11-1-1-1-1-1-1111-1-1-1-111-1-1
χ4111111111111111111111-1-1-1-11111111111111-1-11-1-11-1-1-1-111-1-1-1-111111-1-1-1-111111-1-1-1-1
χ511111-1-111111-1111111111111-1-1-1-111111111111-111-11111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1
χ611111-1-111111-11111111111-1-1-1-1-1-111111-1-1-1-111-111-1-1-1-1-1-1-111-1-11-1-1-1-111-1-1-1111111-1-1
χ711111-1-111111-111111111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-1-111-11111-1-111
χ811111-1-111111-111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-11111
χ9111-11111111-1-11111-1-1-1-11-11-11111-1-11-1-111-1-11-1-11-1-11-11-1-1-11-11-1111-1-11-11-1111-1-11-11-1
χ10111-11111111-1-11111-1-1-1-11-1-111111-1-11-1-1-1-1111-1-11-1-1-11-11-1-1-111-11-1-1111-1-111-1-111-111-1
χ11111-11111111-1-11111-1-1-1-1-111-11111-1-11-1-1-1-111-11-1-11-11-11-1-1-11-1-111-1-111-111-11-1-1111-1-11
χ12111-11111111-1-11111-1-1-1-1-11-111111-1-11-1-111-1-1-11-1-11-1-11-11-1-1-11-11111-1-1-11-11111-1-1-11-11
χ13111-11-1-11111-111111-1-1-1-11-11-1-1-1-1-1-1-11-1-111-1-11-111-111-11-111-11-11111-1-11-11-1-1-1-111-11-11
χ14111-11-1-11111-111111-1-1-1-11-1-11-1-1-1-1-1-11-1-1-1-1111-111-11-11-11111-1-111-1-1111-1-11-111-1-11-1-11
χ15111-11-1-11111-111111-1-1-1-1-111-1-1-1-1-1-1-11-1-1-1-111-111-1111-11-111-111-11-1-111-111-1-111-1-1-111-1
χ16111-11-1-11111-111111-1-1-1-1-11-11-1-1-1-1-1-11-1-111-1-1-111-111-11-11111-11-1111-1-1-11-11-1-1-1111-11-1
χ172222222222222222222-2-20000222222-2-2-200000020020000-2-20000-200000000-200000000
χ1822222-2-222222-2222222-2-20000-2-2-2-222-2-2-2000000-200-20000220000-200000000200000000
χ19222-22222222-2-22222-2-22200002222-2-2-222000000-200-20000220000-200000000-200000000
χ20222-22-2-22222-222222-2-2220000-2-2-2-2-2-2-22200000020020000-2-20000-200000000200000000
χ2122-12-1002222-10-1-1-1-1222222220000-1-12-1-12222-1-10220-1-122000000-1-1-1-1-1-1-1-1-1000000000
χ2222-12-1002222-10-1-1-1-1222222-2-20000-1-12-1-1-2-2-2-2-1-1022011-2-2000000-11111-1-111000000000
χ2322-12-1002222-10-1-1-1-12222-2-2220000-1-12-1-1-2-2-2-2110-2-20-1-122000000-1111111-1-1000000000
χ2422-12-1002222-10-1-1-1-12222-2-2-2-20000-1-12-1-12222110-2-2011-2-2000000-1-1-1-1-11111000000000
χ2522-1-2-100222210-1-1-1-1-2-2-2-22-22-200001121122-2-2-1102-20-112-2000000-1-1-111-11-11000000000
χ2622-1-2-100222210-1-1-1-1-2-2-2-22-2-22000011211-2-222-1102-201-1-22000000-111-1-1-111-1000000000
χ2722-1-2-100222210-1-1-1-1-2-2-2-2-222-2000011211-2-2221-10-220-112-2000000-111-1-11-1-11000000000
χ2822-1-2-100222210-1-1-1-1-2-2-2-2-22-2200001121122-2-21-10-2201-1-22000000-1-1-1111-11-1000000000
χ292-220-22i−2i22-2-20022-2-2002-200002i−2i2i−2i0002-2i2−i2i2−i200000000002i−2i00000i2−i2i2−i2000002−22−20000
χ302-220-22i−2i22-2-20022-2-2002-200002i−2i2i−2i0002-2−i2i2−i2i200000000002i−2i00000−i2i2−i2i200000−22−220000
χ312-220-22i−2i22-2-20022-2-200-2200002i−2i2i−2i000-22i2−i2−i2i20000000000−2i2i00000i2−i2−i2i2000002−2−220000
χ322-220-22i−2i22-2-20022-2-200-2200002i−2i2i−2i000-22−i2i2i2−i20000000000−2i2i00000−i2i2i2−i200000−222−20000
χ332-220-2−2i2i22-2-20022-2-2002-20000−2i2i−2i2i0002-2i2−i2i2−i20000000000−2i2i00000i2−i2i2−i200000−22−220000
χ342-220-2−2i2i22-2-20022-2-2002-20000−2i2i−2i2i0002-2−i2i2−i2i20000000000−2i2i00000−i2i2−i2i2000002−22−20000
χ352-220-2−2i2i22-2-20022-2-200-220000−2i2i−2i2i000-22i2−i2−i2i200000000002i−2i00000i2−i2−i2i200000−222−20000
χ362-220-2−2i2i22-2-20022-2-200-220000−2i2i−2i2i000-22−i2i2i2−i200000000002i−2i00000−i2i2i2−i2000002−2−220000
χ3744444441-2-2144-211-2-21002200-2-2111-20000000221-1-1-2000000002200000-1-1000000000-1-1
χ3844444441-2-2144-211-2-2100-2-200-2-2111-20000000-2-2111-200000000-2-2000001100000000011
χ394444444-211-2441-2-211-200002211-2-2-21000000000-200122-1-10022000000000-1-100000-1-100
χ404444444-211-2441-2-211-20000-2-211-2-2-21000000000-2001-2-21100-2-200000000011000001100
χ4144444-4-41-2-214-4-211-2-2100220022-1-11-2000000022-1-1-1200000000-2-200000-1-100000000011
χ4244444-4-41-2-214-4-211-2-2100-2-20022-1-11-20000000-2-2-111200000000220000011000000000-1-1
χ4344444-4-4-211-24-41-2-211-2000022-1-122-21000000000200-122-1-100-2-2000000000-1-1000001100
χ4444444-4-4-211-24-41-2-211-20000-2-2-1-122-21000000000200-1-2-21100220000000001100000-1-100
χ45444-44441-2-21-4-4-211-22-1002-200-2-211-1200000002-2-1-112000000002-200000-11000000000-11
χ46444-44441-2-21-4-4-211-22-100-2200-2-211-120000000-22-11-1200000000-22000001-10000000001-1
χ47444-4444-211-2-4-41-2-21-1200002-211-2-22-1000000000200-12-2-11002-2000000000-1100000-1100
χ48444-4444-211-2-4-41-2-21-120000-2211-2-22-1000000000200-1-221-100-220000000001-1000001-100
χ49444-44-4-41-2-21-44-211-22-1002-20022-1-1-1200000002-21-11-200000000-2200000-110000000001-1
χ50444-44-4-41-2-21-44-211-22-100-220022-1-1-120000000-2211-1-2000000002-2000001-1000000000-11
χ51444-44-4-4-211-2-441-2-21-1200002-2-1-1222-1000000000-20012-2-1100-22000000000-11000001-100
χ52444-44-4-4-211-2-441-2-21-120000-22-1-1222-1000000000-2001-221-1002-20000000001-100000-1100
χ5344-24-2004444-20-2-2-2-244-4-400000000-2-2-42200000000000000000000200000000000000000
χ5444-2-4-200444420-2-2-2-2-4-4440000000022-4-2-200000000000000000000200000000000000000
χ554-4-2020044-4-400-2-222004-400000000000-222i2−2i22i2−2i200000000000000000−i2i2−i2i20000000000000
χ564-4-2020044-4-400-2-222004-400000000000-22−2i22i2−2i22i200000000000000000i2−i2i2−i20000000000000
χ574-4-2020044-4-400-2-22200-44000000000002-22i2−2i2−2i22i200000000000000000−i2i2i2−i20000000000000
χ584-4-2020044-4-400-2-22200-44000000000002-2−2i22i22i2−2i200000000000000000i2−i2−i2i20000000000000
χ5988-48-4002-4-42-402-1-12-420044000000-120000000-2-20-2-200000000000000001100000000000
χ6088-48-4002-4-42-402-1-12-4200-4-4000000-120000000220220000000000000000-1-100000000000
χ6188-48-400-422-4-40-122-12-400004400002-10000000000000-2-2-2-2000000000000011000000000
χ6288-48-400-422-4-40-122-12-40000-4-400002-1000000000000022220000000000000-1-1000000000
χ6388-4-8-4002-4-42402-1-124-2004-40000001-20000000-220-2200000000000000001-100000000000
χ6488-4-8-4002-4-42402-1-124-200-440000001-200000002-202-20000000000000000-1100000000000
χ6588-4-8-400-422-440-122-1-2400004-40000-210000000000000-22-2200000000000001-1000000000
χ6688-4-8-400-422-440-122-1-240000-440000-2100000000000002-22-20000000000000-11000000000
χ678-880-88i−8i2-44-200-42-2400000000−4i4i2i−2i0000000000000000000000000000000000000000000
χ688-880-88i−8i-42-24002-44-2000000002i−2i−4i4i0000000000000000000000000000000000000000000
χ698-880-8−8i8i2-44-200-42-24000000004i−4i−2i2i0000000000000000000000000000000000000000000
χ708-880-8−8i8i-42-24002-44-200000000−2i2i4i−4i0000000000000000000000000000000000000000000
χ7116-16-808004-88-4004-22-40000000000000000000000000000000000000000000000000000000
χ7216-16-80800-84-4800-24-420000000000000000000000000000000000000000000000000000000

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