Finite Group Databasebeta

← Group #98221

Character table — Group #98221

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444444444444444888888888888888822224488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1111-1-1-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ7111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1
χ911111111-1-1-11111-1-1-1-1-111-1-11111-1-1111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11-1ii−i−iii−i−i
χ1011111111-1-1-11111-1-1-1-1-111-1-11111-1-1111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11-1−i−iii−i−iii
χ1111111111-1-1-11111-1-1-1-1-111-1-11111-1-1111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111-11ii−i−i−i−iii
χ1211111111-1-1-11111-1-1-1-1-111-1-11111-1-1111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111-11−i−iiiii−i−i
χ1311111111-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1111111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1111-1−i−iii−i−iii
χ1411111111-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1111111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1111-1ii−i−iii−i−i
χ1511111111-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-11-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-11−i−iiiii−i−i
χ1611111111-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-11-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11ii−i−i−i−iii
χ17222222222222222-2-2-22-2-2-22-222222-2-2-2-222-2-20000000000000000000000000000000000
χ18222222222222222-2-2-22-2-2-22-2-2-2-2-22-2-222-2-2220000000000000000000000000000000000
χ1922222222222-2-2-2-22222222-2-20000-2-2-2000000222200000000000000000000-2-200000000
χ2022222222222-2-2-2-22222222-2-20000-2-2-2000000-2-2-2-2000000000000000000002200000000
χ2122222222222-2-2-2-2-2-2-22-2-2-2-220000-222000000000000000000000000002-22-20000000000
χ2222222222222-2-2-2-2-2-2-22-2-2-2-220000-22200000000000000000000000000-22-220000000000
χ2322222222-2-2-22222222-22-2-2-222222-22-2-2-2-2-2220000000000000000000000000000000000
χ2422222222-2-2-22222222-22-2-2-22-2-2-2-2-22-22222-2-20000000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2222-22-2-22-200002-22000000000000000000000000002-2-220000000000
χ2622222222-2-2-2-2-2-2-2222-22-2-22-200002-2200000000000000000000000000-222-20000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222000022-200000022-2-200000000000000000000-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222000022-2000000-2-222000000000000000000002-200000000
χ29222-2-2-22-222-200002-2-2-222-20000000000000002i−2i2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000
χ30222-2-2-22-222-200002-2-2-222-20000000000000002i−2i2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000
χ31222-2-2-22-222-200002-2-2-222-2000000000000000−2i2i−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000000000
χ32222-2-2-22-222-200002-2-2-222-2000000000000000−2i2i−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000000000
χ33222-2-2-22-2-2-220000-2222-22-20000000000000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000000000
χ34222-2-2-22-2-2-220000-2222-22-20000000000000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000000000
χ35222-2-2-22-2-2-220000-2222-22-2000000000000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000000000
χ36222-2-2-22-2-2-220000-2222-22-2000000000000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000000000
χ3722-222-2-2-22-2222-2-2000-2000-202i2i−2i−2i200002i−2i00000000000000i2−i2i2−i2i2−i2i2−i200000000002−22−2
χ3822-222-2-2-22-2222-2-2000-2000-202i2i−2i−2i200002i−2i00000000000000−i2i2−i2i2−i2i2−i2i20000000000−22−22
χ3922-222-2-2-22-2222-2-2000-2000-20−2i−2i2i2i20000−2i2i00000000000000i2−i2i2−i2i2−i2i2−i20000000000−22−22
χ4022-222-2-2-22-2222-2-2000-2000-20−2i−2i2i2i20000−2i2i00000000000000−i2i2−i2i2−i2i2−i2i200000000002−22−2
χ4122-222-2-2-2-22-222-2-20002000202i2i−2i−2i-20000−2i2i000000000000002−22−2−22−220000000000−i2i2i2−i2
χ4222-222-2-2-2-22-222-2-20002000202i2i−2i−2i-20000−2i2i00000000000000−22−222−22−20000000000i2−i2−i2i2
χ4322-222-2-2-2-22-222-2-2000200020−2i−2i2i2i-200002i−2i000000000000002−22−2−22−220000000000i2−i2−i2i2
χ4422-222-2-2-2-22-222-2-2000200020−2i−2i2i2i-200002i−2i00000000000000−22−222−22−20000000000−i2i2i2−i2
χ452-2-22-2-2220002-22-222-20-200022-22-20-2000002-20000i2−i2i2−i2i2−i2i2−i200000000000000i2−i2i2−i20000
χ462-2-22-2-2220002-22-222-20-200022-22-20-2000002-20000−i2i2−i2i2−i2i2−i2i200000000000000−i2i2−i2i20000
χ472-2-22-2-2220002-22-222-20-20002-22-220-200000-220000i2−i2i2−i2i2−i2i2−i200000000000000−i2i2−i2i20000
χ482-2-22-2-2220002-22-222-20-20002-22-220-200000-220000−i2i2−i2i2−i2i2−i2i200000000000000i2−i2i2−i20000
χ492-2-22-2-2220002-22-2-2-2202000-22-22-20200000-2200002−22−2−22−22000000000000002−2−220000
χ502-2-22-2-2220002-22-2-2-2202000-22-22-20200000-220000−22−222−22−200000000000000−222−20000
χ512-2-22-2-2220002-22-2-2-2202000-2-22-2202000002-200002−22−2−22−2200000000000000−222−20000
χ522-2-22-2-2220002-22-2-2-2202000-2-22-2202000002-20000−22−222−22−2000000000000002−2−220000
χ53444-4-4-44-444-40000-444-4-4-440000000000000000000000000000000000000000000000000
χ54444-4-4-44-4-4-4400004-4-444-440000000000000000000000000000000000000000000000000
χ5544-444-4-4-44-44-4-444000-4000400000-4000000000000000000000000000000000000000000
χ5644-444-4-4-4-44-4-4-4440004000-4000004000000000000000000000000000000000000000000
χ5744-4-4-44-444-4-4000000040000000000000000000000000000002-2-222-2-2200000000000000
χ5844-4-4-44-444-4-400000004000000000000000000000000000000-222-2-222-200000000000000
χ5944-4-4-44-44-4440000000-40000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ6044-4-4-44-44-4440000000-4000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ614-444-44-4-40004-4-440000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ624-444-44-4-40004-4-44000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ634-444-44-4-4000-444-400000000000000004i−4i00000000000000000000000000000000000000
χ644-444-44-4-4000-444-40000000000000000−4i4i00000000000000000000000000000000000000
χ654-4-44-4-444000-44-4444-40-4000-400000400000000000000000000000000000000000000000
χ664-4-44-4-444000-44-44-4-4404000400000-400000000000000000000000000000000000000000
χ674-4-4-4444-400000004-440-40000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ684-4-4-4444-400000004-440-4000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ694-4-4-4444-40000000-44-4040000000000000000000002-2-22-222-20000000000000000000000
χ704-4-4-4444-40000000-44-404000000000000000000000-222-22-2-220000000000000000000000
χ718-88-88-8-88000000000000000000000000000000000000000000000000000000000000000

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