Finite Group Databasebeta

← Group #308104

Character table — Group #308104

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-111-1-111-1-1-1-1111111111111-1-1-11-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-11111-1-111-1
χ911111111111111111-1-1-1-1111111111111111-1-111-1-111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111
χ1111111111111111111-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111111-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-11111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1111-111-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1111-1-1111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11
χ172222222222-22-2-2-22-200002222-200002222-2-2002200000000-2-200000000-2000000000000
χ182222222222-22-2-2-22-200002222-20000-2-2-2-2-2-200-2-20000000022000000002000000000000
χ192222222222-22-2-2-22-20000-2-2-2-2-2000022222200-2-200000000-2-2000000002000000000000
χ202222222222-22-2-2-22-20000-2-2-2-2-20000-2-2-2-2220022000000002200000000-2000000000000
χ2122222222-2-22-2222-2-222220000-222220000002200-2-20000-2-20000000000000-2000000000
χ2222222222-2-22-2222-2-222220000-2-2-2-2-2000000-2-200-2-200002200000000000002000000000
χ2322222222-2-22-2222-2-2-2-2-2-20000-22222000000-2-200220000-2-200000000000002000000000
χ2422222222-2-22-2222-2-2-2-2-2-20000-2-2-2-2-20000002200220000220000000000000-2000000000
χ25222-2-2-22-2222-2-22-2-2222-2-20000-2000000000000002-222-2-200000000000000002-20000000
χ26222-2-2-22-2222-2-22-2-2222-2-20000-2000000000000002-2-2-2220000000000000000-220000000
χ27222-2-2-22-2222-2-22-2-22-2-2220000-200000000000000-2222-2-20000000000000000-220000000
χ28222-2-2-22-2222-2-22-2-22-2-2220000-200000000000000-22-2-22200000000000000002-20000000
χ29222-2-2-22-2-2-222-22-22-222-2-22i2i−2i−2i2000000002i−2i0000-22000000000000000002i−2i0000000000
χ30222-2-2-22-2-2-222-22-22-222-2-2−2i−2i2i2i200000000−2i2i0000-2200000000000000000−2i2i0000000000
χ31222-2-2-22-2-2-222-22-22-2-2-2222i2i−2i−2i2000000002i−2i00002-200000000000000000−2i2i0000000000
χ32222-2-2-22-2-2-222-22-22-2-2-222−2i−2i2i2i200000000−2i2i00002-2000000000000000002i−2i0000000000
χ33222-2-2-22-2-2-2-222-222200002i2i−2i−2i-200000000−2i2i0000000000000022-2-200000000002i−2i00000
χ34222-2-2-22-2-2-2-222-222200002i2i−2i−2i-200000000−2i2i00000000000000-2-2220000000000−2i2i00000
χ35222-2-2-22-2-2-2-222-22220000−2i−2i2i2i-2000000002i−2i0000000000000022-2-20000000000−2i2i00000
χ36222-2-2-22-2-2-2-222-22220000−2i−2i2i2i-2000000002i−2i00000000000000-2-22200000000002i−2i00000
χ3722-22-2-2-222-20-20002000002-22-2022−2−22i2i−2i−2i00002i−2i002−22−22−2000000i2i2−i2−i200000000i2−i2000
χ3822-22-2-2-222-20-20002000002-22-2022−2−2−2i−2i2i2i0000−2i2i002−22−22−2000000−i2−i2i2i200000000−i2i2000
χ3922-22-2-2-222-20-20002000002-22-20−2−2222i2i−2i−2i00002i−2i00−22−22−22000000−i2−i2i2i200000000−i2i2000
χ4022-22-2-2-222-20-20002000002-22-20−2−222−2i−2i2i2i0000−2i2i00−22−22−22000000i2i2−i2−i200000000i2−i2000
χ4122-22-2-2-222-20-2000200000-22-22022−2−22i2i−2i−2i0000−2i2i00−22−222−2000000i2i2−i2−i200000000−i2i2000
χ4222-22-2-2-222-20-2000200000-22-22022−2−2−2i−2i2i2i00002i−2i00−22−222−2000000−i2−i2i2i200000000i2−i2000
χ4322-22-2-2-222-20-2000200000-22-220−2−2222i2i−2i−2i0000−2i2i002−22−2−22000000−i2−i2i2i200000000i2−i2000
χ4422-22-2-2-222-20-2000200000-22-220−2−222−2i−2i2i2i00002i−2i002−22−2−22000000i2i2−i2−i200000000−i2i2000
χ452-2-2-22-22200202-2-2002i−2i2i−2i000002-22-22−22−2002i−2i00000000002−2i2−i2i2−i22−22−20000000000i2−i20
χ462-2-2-22-22200202-2-2002i−2i2i−2i000002-22-2−22−22002i−2i0000000000−22−i2i2−i2i2−22−220000000000−i2i20
χ472-2-2-22-22200202-2-2002i−2i2i−2i00000-22-222−22−200−2i2i00000000002−2i2−i2i2−i2−22−220000000000−i2i20
χ482-2-2-22-22200202-2-2002i−2i2i−2i00000-22-22−22−2200−2i2i0000000000−22−i2i2−i2i22−22−20000000000i2−i20
χ492-2-2-22-22200202-2-200−2i2i−2i2i000002-22-22−22−200−2i2i00000000002−2−i2i2−i2i22−22−20000000000−i2i20
χ502-2-2-22-22200202-2-200−2i2i−2i2i000002-22-2−22−2200−2i2i0000000000−22i2−i2i2−i2−22−220000000000i2−i20
χ512-2-2-22-22200202-2-200−2i2i−2i2i00000-22-222−22−2002i−2i00000000002−2−i2i2−i2i2−22−220000000000i2−i20
χ522-2-2-22-22200202-2-200−2i2i−2i2i00000-22-22−22−22002i−2i0000000000−22i2−i2i2−i22−22−20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-4-44-444-4-44-44-4-4000000004000000000000000000000000000000000000000000000
χ5544-44-4-4-44-4404000-400000000002222−22−220000000000000000−222200000000000000000000000
χ5644-44-4-4-44-4404000-40000000000−22−222222000000000000000022−2200000000000000000000000
χ5744-4-444-4-44-404000-40000000000000000000000000022−22−22220000000000000000000000000
χ5844-4-444-4-44-404000-400000000000000000000000000−222222−220000000000000000000000000
χ5944-4-444-4-4-440-40004000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ6044-4-444-4-4-440-4000400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ614-44-4-44-4400000000000000000022−22−22222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ624-44-4-44-4400000000000000000022−22−2222−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ634-44-4-44-44000000000000000000−222222−222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ644-44-4-44-44000000000000000000−222222−22−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ654-4-44-444-40040-4-44004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ664-4-44-444-40040-4-4400−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ674-4-44-444-400-4044-4000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ684-4-44-444-400-4044-400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ694-4-4-44-44400-40-44400000000000000022−2222−2200000000000000−2222000000000000000000000
χ704-4-4-44-44400-40-444000000000000000−2222−22220000000000000022−22000000000000000000000
χ718-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000

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