Finite Group Databasebeta

← Group #267104

Character table — Group #267104

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444448888888822244888888888888888888882244888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ9111111111-1-1-1-11111111-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-11-1
χ10111111111-1-1-1-11111111-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-111-11
χ11111111111-1-1-1-11111111-1-1111111-1-11111-1-1-1-11111-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ12111111111-1-1-1-11111111-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-11-1
χ13111111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ14111111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1111-1
χ15111111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1111-1
χ16111111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-111-1-1-11
χ172222222222222-2-222-2-22-2-22222-2-222-2-2-2-200000000-2-2-222000000000000000000000000000000
χ182222222222222-2-222-2-22-2-2-2-2-2-2-2-222222200000000-222-2-2000000000000000000000000000000
χ19222222222-2-2-2-2-2-222-2-22222222-2-2-2-2-2-2-2-200000000222-2-2000000000000000000000000000000
χ20222222222-2-2-2-2-2-222-2-2222-2-2-2-2-2-2-2-22222000000002-2-222000000000000000000000000000000
χ2122222222-2222222-2-222-2220000-2-2-2-2000022222222-200000000-2-2-2-20000000000000000000000
χ2222222222-2222222-2-222-2220000-2-2-2-20000-2-2-2-2-2-2-2-2-20000000022220000000000000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-2000022-2-200000000000020000000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2422222222-22222-2-2-2-2-2-2-2-2-2000022-2-20000000000002000000000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2522222222-2-2-2-2-222-2-222-2-2-20000-2-22200002222-2-2-2-2200000000-2-2220000000000000000000000
χ2622222222-2-2-2-2-222-2-222-2-2-20000-2-2220000-2-2-2-2222220000000022-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22200002222000000000000-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22200002222000000000000-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ29222-2-2-22-202i2i−2i−2i2-2002-202i−2i0000000000002i2i−2i−2i22-2-200000i2i2−i2−i200000000000022−2−200002−2i2−i200
χ30222-2-2-22-202i2i−2i−2i2-2002-202i−2i0000000000002i2i−2i−2i22-2-200000−i2−i2i2i2000000000000−2−2220000−22−i2i200
χ31222-2-2-22-202i2i−2i−2i2-2002-202i−2i000000000000−2i−2i2i2i-2-22200000i2i2−i2−i200000000000022−2−20000−22−i2i200
χ32222-2-2-22-202i2i−2i−2i2-2002-202i−2i000000000000−2i−2i2i2i-2-22200000−i2−i2i2i2000000000000−2−22200002−2i2−i200
χ33222-2-2-22-20−2i−2i2i2i2-2002-20−2i2i0000000000002i2i−2i−2i-2-22200000i2i2−i2−i2000000000000−2−22200002−2−i2i200
χ34222-2-2-22-20−2i−2i2i2i2-2002-20−2i2i0000000000002i2i−2i−2i-2-22200000−i2−i2i2i200000000000022−2−20000−22i2−i200
χ35222-2-2-22-20−2i−2i2i2i2-2002-20−2i2i000000000000−2i−2i2i2i22-2-200000i2i2−i2−i2000000000000−2−2220000−22i2−i200
χ36222-2-2-22-20−2i−2i2i2i2-2002-20−2i2i000000000000−2i−2i2i2i22-2-200000−i2−i2i2i200000000000022−2−200002−2−i2i200
χ3722-2-222-2-222i−2i2i−2i00-2-2002000000002i−2i2i2i−2i−2i2−22−2i2−i2i2−i202-20000002−2i2−i2i2−i2i2−i22−22−200000000000000
χ3822-2-222-2-222i−2i2i−2i00-2-2002000000002i−2i2i2i−2i−2i−22−22−i2i2−i2i202-2000000−22−i2i2−i2i2−i2i2−22−2200000000000000
χ3922-2-222-2-222i−2i2i−2i00-2-2002000000002i−2i−2i−2i2i2i2−22−2i2−i2i2−i20-220000002−2i2−i2−i2i2−i2i2−22−2200000000000000
χ4022-2-222-2-222i−2i2i−2i00-2-2002000000002i−2i−2i−2i2i2i−22−22−i2i2−i2i20-22000000−22−i2i2i2−i2i2−i22−22−200000000000000
χ4122-2-222-2-22−2i2i−2i2i00-2-200200000000−2i2i2i2i−2i−2i2−22−2−i2i2−i2i20-220000002−2−i2i2i2−i2i2−i2−22−2200000000000000
χ4222-2-222-2-22−2i2i−2i2i00-2-200200000000−2i2i2i2i−2i−2i−22−22i2−i2i2−i20-22000000−22i2−i2−i2i2−i2i22−22−200000000000000
χ4322-2-222-2-22−2i2i−2i2i00-2-200200000000−2i2i−2i−2i2i2i2−22−2−i2i2−i2i202-20000002−2−i2i2−i2i2−i2i22−22−200000000000000
χ4422-2-222-2-22−2i2i−2i2i00-2-200200000000−2i2i−2i−2i2i2i−22−22i2−i2i2−i202-2000000−22i2−i2i2−i2i2−i2−22−2200000000000000
χ4522-2-222-2-2-22i−2i2i−2i002200-20022-2-200−2i2i00002−22−2i2−i2i2−i20002i−2i0000−22−i2i22−2−22−i2i2i2−i200000000000000
χ4622-2-222-2-2-22i−2i2i−2i002200-20022-2-200−2i2i0000−22−22−i2i2−i2i20002i−2i00002−2i2−i2−222−2i2−i2−i2i200000000000000
χ4722-2-222-2-2-22i−2i2i−2i002200-200-2-22200−2i2i00002−22−2i2−i2i2−i2000−2i2i0000−22−i2i2−222−2i2−i2−i2i200000000000000
χ4822-2-222-2-2-22i−2i2i−2i002200-200-2-22200−2i2i0000−22−22−i2i2−i2i2000−2i2i00002−2i2−i22−2−22−i2i2i2−i200000000000000
χ4922-2-222-2-2-2−2i2i−2i2i002200-20022-2-2002i−2i00002−22−2−i2i2−i2i2000−2i2i0000−22i2−i22−2−22i2−i2−i2i200000000000000
χ5022-2-222-2-2-2−2i2i−2i2i002200-20022-2-2002i−2i0000−22−22i2−i2i2−i2000−2i2i00002−2−i2i2−222−2−i2i2i2−i200000000000000
χ5122-2-222-2-2-2−2i2i−2i2i002200-200-2-222002i−2i00002−22−2−i2i2−i2i20002i−2i0000−22i2−i2−222−2−i2i2i2−i200000000000000
χ5222-2-222-2-2-2−2i2i−2i2i002200-200-2-222002i−2i0000−22−22i2−i2i2−i20002i−2i00002−2−i2i22−2−22i2−i2−i2i200000000000000
χ532-2-2-22-222-200002-22-2-222002-22-22-2002-22-200000000000002-22-200000000000000002-200000000
χ542-2-2-22-222-200002-22-2-222002-22-22-2002-22-20000000000000-22-220000000000000000-2200000000
χ552-2-2-22-222-200002-22-2-22200-22-222-200-22-2200000000000002-22-20000000000000000-2200000000
χ562-2-2-22-222-200002-22-2-22200-22-222-200-22-220000000000000-22-2200000000000000002-200000000
χ572-2-2-22-222-20000-222-22-22002-22-2-2200-22-22000000000000000000000000000002-22-2002-2000000
χ582-2-2-22-222-20000-222-22-22002-22-2-2200-22-2200000000000000000000000000000-22-2200-22000000
χ592-2-2-22-222-20000-222-22-2200-22-22-22002-22-2000000000000000000000000000002-22-200-22000000
χ602-2-2-22-222-20000-222-22-2200-22-22-22002-22-200000000000000000000000000000-22-22002-2000000
χ61444-4-4-44-404i4i−4i−4i-4400-440−4i4i0000000000000000000000000000000000000000000000000000000
χ62444-4-4-44-40−4i−4i4i4i-4400-4404i−4i0000000000000000000000000000000000000000000000000000000
χ6344-44-4-4-4404-4-440000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ6444-44-4-4-4404-4-44000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ6544-44-4-4-440-444-40000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ6644-44-4-4-440-444-4000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ674-4444-4-4-440000004-400-4004-4-44000000000000000000000000000000000000000000000000000
χ684-4444-4-4-440000004-400-400-444-4000000000000000000000000000000000000000000000000000
χ694-4444-4-4-4-4000000-4400400000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ704-4444-4-4-4-4000000-440040000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ714-4-44-444-4000004400-4-400000000000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ724-4-44-444-4000004400-4-40000000000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ734-4-44-444-400000-4-400440000000000000000000000000000000000000000000022−22−22220000000000
χ744-4-44-444-400000-4-4004400000000000000000000000000000000000000000000−222222−220000000000
χ754-4-4-44-444400004-4-44-44-4000000-440000000000000000000000000000000000000000000000000
χ764-4-4-44-44440000-44-444-4-40000004-40000000000000000000000000000000000000000000000000
χ778-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000000

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