Finite Group Databasebeta

← Group #72337749

Character table — Group #72337749

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112244444488888888881616161616161616161616161616161616323232323232323232323232323232323232323232326464646464646464646464128128
order12222222222222222222222222222244444444444444444444444444444444444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111-1-11111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1111111
χ5111111111111111111-1-111111-111-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-1111111-1-11-1-111-1-111-1-11-1
χ6111111111111111111-1-111111-111-1-1-1-1-1-1-1-11111-111-1-111-1-1-1-111-1-1-1-1-1-11111-111-1-1-1-111-11
χ7111111111111111111-1-111111-1-1-111-1-11111111-11-1-1-1-1-1-111-1-1-1-1111111-1-11-1-1-1-111-1-111-11
χ8111111111111111111-1-111111-1-1-111-1-1-1-1-1-1111-1111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-11111-1-11-1
χ911111111111111-1-1-1-111111-1-11111111111111111-1-1111111-1-1-1-111-1-1-1-111-11-1-1-1-1-11111-1-1
χ1011111111111111-1-1-1-111111-1-11111111-1-1-1-11111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111
χ1111111111111111-1-1-1-111111-1-11-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-11-11111-1-1-1-111
χ1211111111111111-1-1-1-111111-1-11-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-111111111-1-1
χ1311111111111111-1-1-1-1-1-1111-1-1-111-1-1-1-111111111-111-1-111-1-1111111-1-1-1-1-1-1-1-11-1-11111-1-1-11
χ1411111111111111-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-111-1-1-1-1111111-111-1-111-1-1111-1
χ1511111111111111-1-1-1-1-1-1111-1-1-1-1-111-1-11111111-1111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1
χ1611111111111111-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-1-1111-11-1-1-1-1-1-11111-1-1-1-1111111-11111-1-111-1-1-11
χ172222222222222222222222-222-200002-20000-2-2-200002-20000220000000000-20-20000000000
χ18222222222222222222-2-222-22220000-220000-2-2-20000-220000-2-20000000000-2020000000000
χ1922222222222222-2-2-2-22222-2-2-2-200002-20000-2-2-200002-20000-2-200000000002020000000000
χ2022222222222222-2-2-2-2-2-222-2-2-220000-220000-2-2-20000-22000022000000000020-20000000000
χ21222222222222-2-2000022-2-220020000222222-2-220000-2-200000000-2-20000220-200000000000
χ22222222222222-2-2000022-2-22002000022-2-2-2-2-2-220000-2-200000000220000-2-20200000000000
χ23222222222222-2-2000022-2-2-200-200002-2000022-20022-22000000-2-20022-2-2000000000000000
χ24222222222222-2-2000022-2-2-200-200002-2000022-200-2-2-220000002200-2-222000000000000000
χ25222222222222-2-20000-2-2-2-2200-20000-2-22222-2-2200002200000000-2-20000-2-20200000000000
χ26222222222222-2-20000-2-2-2-2200-20000-2-2-2-2-2-2-2-2200002200000000220000220-200000000000
χ27222222222222-2-20000-2-2-2-2-20020000-22000022-200222-2000000-2-200-2-222000000000000000
χ28222222222222-2-20000-2-2-2-2-20020000-22000022-200-2-22-2000000220022-2-2000000000000000
χ2922222222-2-2-2-22-20000002-220000022002i2i−2i−2i2-2-202000000-2-200002i−2i0000000000000002i−2i00
χ3022222222-2-2-2-22-20000002-22000002200−2i−2i2i2i2-2-202000000-2-20000−2i2i000000000000000−2i2i00
χ3122222222-2-2-2-22-20000002-2200000-2-2002i2i−2i−2i2-2-20-20000002200002i−2i000000000000000−2i2i00
χ3222222222-2-2-2-22-20000002-2200000-2-200−2i−2i2i2i2-2-20-2000000220000−2i2i0000000000000002i−2i00
χ3322222222-2-2-2-2-22000000-2220002200002i2i−2i−2i-22-2200000-2-2000000−2i2i00000000000002i−2i0000
χ3422222222-2-2-2-2-22000000-222000220000−2i−2i2i2i-22-2200000-2-20000002i−2i0000000000000−2i2i0000
χ3522222222-2-2-2-2-22000000-222000-2-200002i2i−2i−2i-22-2-20000022000000−2i2i0000000000000−2i2i0000
χ3622222222-2-2-2-2-22000000-222000-2-20000−2i−2i2i2i-22-2-200000220000002i−2i00000000000002i−2i0000
χ3744444444-4-4-4-44-40000004-4-40000000000000-44400000000000000000000000000000000000
χ3844444444-4-4-4-4-44000000-44-400000000000004-4400000000000000000000000000000000000
χ39444444-4-44-44-40000000000000422220-40000000-2-200002-22-20000000000000000000000000
χ40444444-4-44-44-400000000000004-2-2-2-20-40000000220000-22-220000000000000000000000000
χ41444444-4-44-44-40000000000000-422-2-2040000000-2200002-2-220000000000000000000000000
χ42444444-4-44-44-40000000000000-4-2-2220400000002-20000-222-20000000000000000000000000
χ43444444-4-4-44-44000000440000002222-400000000-2-20000-22-220000000000000000000000000
χ44444444-4-4-44-4400000044000000-2-2-2-2-4000000002200002-22-20000000000000000000000000
χ45444444-4-4-44-44000000-4-400000022-2-2400000000-220000-222-20000000000000000000000000
χ46444444-4-4-44-44000000-4-4000000-2-2224000000002-200002-2-220000000000000000000000000
χ4744-4-44-400040-40022-2-24-40002-200000002i−2i2i−2i00000000000002-22i−2i00002i−2i2i−2i0000000000000
χ4844-4-44-400040-40022-2-24-40002-20000000−2i2i−2i2i00000000000002-2−2i2i0000−2i2i−2i2i0000000000000
χ4944-4-44-400040-40022-2-2-440002-200000002i−2i2i−2i0000000000000-22−2i2i00002i−2i−2i2i0000000000000
χ5044-4-44-400040-40022-2-2-440002-20000000−2i2i−2i2i0000000000000-222i−2i0000−2i2i2i−2i0000000000000
χ5144-4-44-400040-400-2-2224-4000-2200000002i−2i2i−2i0000000000000-22−2i2i0000−2i2i2i−2i0000000000000
χ5244-4-44-400040-400-2-2224-4000-220000000−2i2i−2i2i0000000000000-222i−2i00002i−2i−2i2i0000000000000
χ5344-4-44-400040-400-2-222-44000-2200000002i−2i2i−2i00000000000002-22i−2i0000−2i2i−2i2i0000000000000
χ5444-4-44-400040-400-2-222-44000-220000000−2i2i−2i2i00000000000002-2−2i2i00002i−2i2i−2i0000000000000
χ558888-8-88-80000000000000000000000000000000004-40000000000000000000000000000000
χ568888-8-88-8000000000000000000000000000000000-440000000000000000000000000000000
χ578888-8-8-88000000444400000-4-40000000000000000000000000000000000000000000000000
χ588888-8-8-88000000-4-4-4-400000440000000000000000000000000000000000000000000000000
χ5988-8-88-8000-808000000000000000000004-4-4400000000000000000000000000000000000000
χ6088-8-88-8000-80800000000000000000000-444-400000000000000000000000000000000000000
χ6188-8-8-880080-8000000000000000000000000000000000000000000004i−4i00000000000000000
χ6288-8-8-880080-800000000000000000000000000000000000000000000−4i4i00000000000000000
χ6388-8-8-8800-80800044-4-400000-440000000000000000000000000000000000000000000000000
χ6488-8-8-8800-808000-4-444000004-40000000000000000000000000000000000000000000000000
χ658-88-8000000000-44-44-4000400004-40000000000000000000000000000000000002-200000000
χ668-88-8000000000-44-44-400040000-44000000000000000000000000000000000000-2200000000
χ678-88-8000000000-4-44-44000400004-4000000000000000000000000000000000000-2200000000
χ688-88-8000000000-4-44-4400040000-440000000000000000000000000000000000002-200000000
χ698-8-8800000000-404-4-4400400000004-40000000000000000000000000000000000002-2000000
χ708-8-8800000000-404-4-440040000000-44000000000000000000000000000000000000-22000000
χ718-8-8800000000-40-444-400400000004-4000000000000000000000000000000000000-22000000
χ728-8-8800000000-40-444-40040000000-440000000000000000000000000000000000002-2000000
χ7316-1616-1600000000080000000-80000000000000000000000000000000000000000000000000000
χ7416-16-16160000000080000000-800000000000000000000000000000000000000000000000000000

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