Finite Group Databasebeta

← Group #102309

Character table — Group #102309

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222222244444444444444444488888888888888884444444488888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ911111111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-1
χ1011111111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111
χ1111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111
χ1211111111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-1
χ1311111111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ1411111111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ1511111111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ1611111111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ172222222222222222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ182222222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ19222222222222-2-2-2-222-2-2-2-222-2-2-2-222000000000000000022-2-222-2-200000000000000000000
χ20222222222222-2-2-2-222-2-2-2-222-2-2-2-2220000000000000000-2-222-2-22200000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2322222222-2-2-2-222-2-22222-2-222-2-222-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2422222222-2-2-2-222-2-22222-2-222-2-222-2-2-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-22222-2-2222222-2-2-2-200000000000000000000000022-2-2-2-222000000000000
χ2622222222-2-2-2-2-2-22222-2-2222222-2-2-2-2000000000000000000000000-2-22222-2-2000000000000
χ2722222222-2-2-2-2-2-222-2-2-2-222-2-2-2-2222200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ2822222222-2-2-2-2-2-222-2-2-2-222-2-2-2-222220000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ29222-22-2-2-222-2-22-222002-2-2-200000000000022-2-2000022-2-200000000000000002−22−22−22−20000
χ30222-22-2-2-222-2-22-222002-2-2-200000000000022-2-2000022-2-20000000000000000−22−22−22−220000
χ31222-22-2-2-222-2-22-222002-2-2-2000000000000-2-2220000-2-22200000000000000002−22−2−22−220000
χ32222-22-2-2-222-2-22-222002-2-2-2000000000000-2-2220000-2-2220000000000000000−22−222−22−20000
χ33222-22-2-2-2-2-2222-2-2-2002-22200000000000022-2-20000-2-2220000000000000000i2−i2−i2i2i2−i2−i2i20000
χ34222-22-2-2-2-2-2222-2-2-2002-22200000000000022-2-20000-2-2220000000000000000−i2i2i2−i2−i2i2i2−i20000
χ35222-22-2-2-2-2-2222-2-2-2002-222000000000000-2-222000022-2-20000000000000000i2−i2−i2i2−i2i2i2−i20000
χ36222-22-2-2-2-2-2222-2-2-2002-222000000000000-2-222000022-2-20000000000000000−i2i2i2−i2i2−i2−i2i20000
χ3722-2-2-2-2222-22-20000220000-2-200002-222−2−22−22−222−2−22−22−2002i−2i002i−2ii2−i2i2−i2i2−i2i2−i2000000000000
χ3822-2-2-2-2222-22-20000220000-2-200002-222−2−22−22−222−2−22−22−200−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i2000000000000
χ3922-2-2-2-2222-22-20000220000-2-200002-2−2−222−22−22−2−222−22−22002i−2i002i−2i−i2i2−i2i2−i2i2−i2i2000000000000
χ4022-2-2-2-2222-22-20000220000-2-200002-2−2−222−22−22−2−222−22−2200−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i2000000000000
χ4122-2-2-2-2222-22-20000-2-20000220000-2222−2−2−22−2222−2−2−22−222-2002-2002−2−222−2−22000000000000
χ4222-2-2-2-2222-22-20000-2-20000220000-2222−2−2−22−2222−2−2−22−22-2200-2200−222−2−222−2000000000000
χ4322-2-2-2-2222-22-20000-2-20000220000-22−2−2222−22−2−2−2222−22−22-2002-200−222−2−222−2000000000000
χ4422-2-2-2-2222-22-20000-2-20000220000-22−2−2222−22−2−2−2222−22−2-2200-22002−2−222−2−22000000000000
χ4522-2-2-2-222-22-220000220000-2-20000-2222−2−2−22−22−2−2222−22−22i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i2000000000000
χ4622-2-2-2-222-22-220000220000-2-20000-2222−2−2−22−22−2−2222−22−2−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i2000000000000
χ4722-2-2-2-222-22-220000220000-2-20000-22−2−2222−22−222−2−2−22−222i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i2000000000000
χ4822-2-2-2-222-22-220000220000-2-20000-22−2−2222−22−222−2−2−22−22−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i2000000000000
χ4922-2-2-2-222-22-220000-2-200002200002-222−2−22−22−2−2−222−22−22002-200-222−22−2−22−22000000000000
χ5022-2-2-2-222-22-220000-2-200002200002-222−2−22−22−2−2−222−22−2200-22002-2−22−222−22−2000000000000
χ5122-2-2-2-222-22-220000-2-200002200002-2−2−222−22−2222−2−22−22−2002-200-22−22−222−22−2000000000000
χ5222-2-2-2-222-22-220000-2-200002200002-2−2−222−22−2222−2−22−22−200-22002-22−22−2−22−22000000000000
χ53444-44-4-4-444-4-4-44-4-400-44440000000000000000000000000000000000000000000000000000
χ54444-44-4-4-4-4-444-444400-44-4-40000000000000000000000000000000000000000000000000000
χ5544-44-44-4-44-4-44000000000000000000000022−22−2222000022−22−22220000000000000000000000000000
χ5644-44-44-4-44-4-440000000000000000000000−222222−220000−222222−220000000000000000000000000000
χ5744-44-44-4-4-444-4000000000000000000000022−22−22220000−222222−220000000000000000000000000000
χ5844-44-44-4-4-444-40000000000000000000000−222222−22000022−22−22220000000000000000000000000000
χ594-444-4-4-440000004i−4i00004i−4i0000000022−2222−2200002i2−2i22i2−2i200000000000000000000000000000000
χ604-444-4-4-440000004i−4i00004i−4i00000000−2222−22220000−2i22i2−2i22i200000000000000000000000000000000
χ614-444-4-4-44000000−4i4i0000−4i4i0000000022−2222−220000−2i22i2−2i22i200000000000000000000000000000000
χ624-444-4-4-44000000−4i4i0000−4i4i00000000−2222−222200002i2−2i22i2−2i200000000000000000000000000000000
χ634-44-4-444-40000004i−4i4i−4i00−4i4i4i−4i4-4000000000000000000000000000000000000000000000000
χ644-44-4-444-40000004i−4i−4i4i00−4i4i−4i4i-44000000000000000000000000000000000000000000000000
χ654-44-4-444-4000000−4i4i4i−4i004i−4i4i−4i-44000000000000000000000000000000000000000000000000
χ664-44-4-444-4000000−4i4i−4i4i004i−4i−4i4i4-4000000000000000000000000000000000000000000000000
χ674-4-444-44-400004-4004i−4i-4400−4i4i004i−4i0000000000000000000000000000000000000000000000
χ684-4-444-44-400004-400−4i4i-44004i−4i00−4i4i0000000000000000000000000000000000000000000000
χ694-4-444-44-40000-44004i−4i4-400−4i4i00−4i4i0000000000000000000000000000000000000000000000
χ704-4-444-44-40000-4400−4i4i4-4004i−4i004i−4i0000000000000000000000000000000000000000000000
χ714-4-4-444-440000440000-4-40000000000000000004i−4i−4i4i00000000000000000000000000000000
χ724-4-4-444-440000440000-4-4000000000000000000−4i4i4i−4i00000000000000000000000000000000
χ734-4-4-444-440000-4-400004400000000004-4-440000000000000000000000000000000000000000
χ744-4-4-444-440000-4-40000440000000000-444-40000000000000000000000000000000000000000

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