Finite Group Databasebeta

← Group #308072

Character table — Group #308072

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-1-1-11-1-111-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-111-1-1-1-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111-1-1-11111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-111-1-1111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111111-1-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1111111111-1-1111-1-1-1-1-1-11
χ17222222222-2-2222-2-2-222220000-222220000-2-22200000000-2-2000000000000000-20000000
χ18222222222-2-2222-2-2-222220000-2-2-2-2-20000-2-2-2-2000000002200000000000000020000000
χ19222222222-2-2222-2-2-2-2-2-2-20000-22222000022-2-200000000-2-200000000000000020000000
χ20222222222-2-2222-2-2-2-2-2-2-20000-2-2-2-2-2000022220000000022000000000000000-20000000
χ2122222222-222-2-2-222-200002222-2000022220000-2-222000000-2-200000000-2000000000000
χ2222222222-222-2-2-222-200002222-20000-2-2-2-20000-2-2-2-200000022000000002000000000000
χ2322222222-222-2-2-222-20000-2-2-2-2-200002222000022-2-2000000-2-2000000002000000000000
χ2422222222-222-2-2-222-20000-2-2-2-2-20000-2-2-2-2000022220000002200000000-2000000000000
χ25222-22-2-2-2222-22-2-2-2222-2-20000-2000000002-200000022-2-200000000000002-20000000000
χ26222-22-2-2-2222-22-2-2-2222-2-20000-2000000002-2000000-2-2220000000000000-220000000000
χ27222-22-2-2-2222-22-2-2-22-2-2220000-200000000-2200000022-2-20000000000000-220000000000
χ28222-22-2-2-2222-22-2-2-22-2-2220000-200000000-22000000-2-22200000000000002-20000000000
χ29222-22-2-2-22-2-2-22-222-222-2-22i2i−2i−2i200000000-22002i−2i0000000000000000000002i−2i00000000
χ30222-22-2-2-22-2-2-22-222-222-2-2−2i−2i2i2i200000000-2200−2i2i000000000000000000000−2i2i00000000
χ31222-22-2-2-22-2-2-22-222-2-2-2222i2i−2i−2i2000000002-2002i−2i000000000000000000000−2i2i00000000
χ32222-22-2-2-22-2-2-22-222-2-2-222−2i−2i2i2i2000000002-200−2i2i0000000000000000000002i−2i00000000
χ33222-22-2-2-2-2-2-22-2222200002i2i−2i−2i-2000000000000−2i2i000000000022-2-200000000002i−2i00000
χ34222-22-2-2-2-2-2-22-2222200002i2i−2i−2i-2000000000000−2i2i0000000000-2-2220000000000−2i2i00000
χ35222-22-2-2-2-2-2-22-222220000−2i−2i2i2i-20000000000002i−2i000000000022-2-20000000000−2i2i00000
χ36222-22-2-2-2-2-2-22-222220000−2i−2i2i2i-20000000000002i−2i0000000000-2-22200000000002i−2i00000
χ3722-2-2-22-22-20022-20002i−2i2i−2i0000022-2-2i2i2−i2−i2002i−2i0000000000i2−i22−22−2i2i2−i2−i2000000002−2000
χ3822-2-2-22-22-20022-20002i−2i2i−2i0000022-2-2−i2−i2i2i2002i−2i0000000000−i2i2−22−22−i2−i2i2i200000000−22000
χ3922-2-2-22-22-20022-20002i−2i2i−2i00000-2-222i2i2−i2−i200−2i2i0000000000i2−i22−22−2−i2−i2i2i200000000−22000
χ4022-2-2-22-22-20022-20002i−2i2i−2i00000-2-222−i2−i2i2i200−2i2i0000000000−i2i2−22−22i2i2−i2−i2000000002−2000
χ4122-2-2-22-22-20022-2000−2i2i−2i2i0000022-2-2i2i2−i2−i200−2i2i0000000000i2−i2−22−22i2i2−i2−i200000000−22000
χ4222-2-2-22-22-20022-2000−2i2i−2i2i0000022-2-2−i2−i2i2i200−2i2i0000000000−i2i22−22−2−i2−i2i2i2000000002−2000
χ4322-2-2-22-22-20022-2000−2i2i−2i2i00000-2-222i2i2−i2−i2002i−2i0000000000i2−i2−22−22−i2−i2i2i2000000002−2000
χ4422-2-2-22-22-20022-2000−2i2i−2i2i00000-2-222−i2−i2i2i2002i−2i0000000000−i2i22−22−2i2i2−i2−i200000000−22000
χ452-2-222-2-2202-20002-2000002-22-20i2−i2i2−i22i−2i2i−2i0000002i−2ii2−i2i2−i2i2−i20000002−22−200000000002−20
χ462-2-222-2-2202-20002-2000002-22-20i2−i2i2−i2−2i2i−2i2i000000−2i2ii2−i2i2−i2i2−i2000000−22−220000000000−220
χ472-2-222-2-2202-20002-2000002-22-20−i2i2−i2i22i−2i2i−2i0000002i−2i−i2i2−i2i2−i2i2000000−22−220000000000−220
χ482-2-222-2-2202-20002-2000002-22-20−i2i2−i2i2−2i2i−2i2i000000−2i2i−i2i2−i2i2−i2i20000002−22−200000000002−20
χ492-2-222-2-2202-20002-200000-22-220i2−i2i2−i22i−2i2i−2i000000−2i2i−i2i2−i2i2i2−i20000002−22−20000000000−220
χ502-2-222-2-2202-20002-200000-22-220i2−i2i2−i2−2i2i−2i2i0000002i−2i−i2i2−i2i2i2−i2000000−22−2200000000002−20
χ512-2-222-2-2202-20002-200000-22-220−i2i2−i2i22i−2i2i−2i000000−2i2ii2−i2i2−i2−i2i2000000−22−2200000000002−20
χ522-2-222-2-2202-20002-200000-22-220−i2i2−i2i2−2i2i−2i2i0000002i−2ii2−i2i2−i2−i2i20000002−22−20000000000−220
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-44-4-4-4-4444-44-4-4-4000000004000000000000000000000000000000000000000000000
χ5544-44-4-44-44004-4-400000000000000000000000000000000000022−22−222200000000000000000
χ5644-44-4-44-44004-4-4000000000000000000000000000000000000−222222−2200000000000000000
χ5744-44-4-44-4-400-4440004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ5844-44-4-44-4-400-444000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ5944-4-4-44-44400-4-4400000000000000002i22i2−2i2−2i200000000000000−2i22i2000000000000000000000
χ6044-4-4-44-44400-4-440000000000000000−2i2−2i22i22i2000000000000002i2−2i2000000000000000000000
χ614-44-4-4-4440000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ624-44-4-4-4440000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ634-44-4-4-444000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ644-44-4-4-444000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ654-4-444-4-440-44000-4400000000002i2−2i22i2−2i20000000000000000−2i22i200000000000000000000000
χ664-4-444-4-440-44000-440000000000−2i22i2−2i22i200000000000000002i2−2i200000000000000000000000
χ674-4-4-4444-404-4000-44000000000000000000000000002i2−2i2−2i22i20000000000000000000000000
χ684-4-4-4444-404-4000-4400000000000000000000000000−2i22i22i2−2i20000000000000000000000000
χ694-4-4-4444-40-440004-4000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ704-4-4-4444-40-440004-400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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