Finite Group Databasebeta

← Group #7125478

Character table — Group #7125478

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111111112222222244444444444444444444444444444444888888888888888888888888816161616161616161616
order12222222444444442244444444444444888888888888888822244444444444444888888882444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1111111
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1111-1-1-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-111-1-111-1-11111111-11111-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-111-1-111-1-1-1-1111111-11-1-1-1-11111
χ9111111111111111111-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-11-11-1
χ10111111111111111111-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-111111111-1-11111-1-11-1-1-1-11-11-11
χ11111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-111-1-1111-1-1-111-1-11111-1-1-1-111-11-1-11-1-11-11
χ12111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11-111-1-111-1-111-1-1-1-1111-111-111-11-1
χ13111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111111111111-1-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11-11-11-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111111-1-1-1-111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-11-11
χ15111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-111-1-1111111-1-1-1-1111-1-11-11
χ16111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-111-11-1-111-1-111111111-1-111-1-1-111-11-1
χ17111111111-1-1-1-1111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-11111-1-1111111-11-1-111-1-1
χ18111111111-1-1-1-1111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-111-1-1-1-11111-1-111-1-11111-1-11-111-1-111
χ19111111111-1-1-1-1111-1-111-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-111
χ20111111111-1-1-1-1111-1-111-1-1111111-1-1-1-1-1-1-1-11111111111111-1-11-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-111111-1-1
χ21111111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1111-11111-1-11111-1-11111-1-1-1-11-11-1-1-111-1-1
χ22111111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-11-1-1-11111-1-1-1-1111111-1-1-1-1-11-1111-1-111
χ23111111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111-11111-1-1-1-11111-1-1-1-111111-1-11-1-1-1-111
χ24111111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1-1-1-11111-111-11111-1-1
χ25111111111-1-1-1-1111-1-1-1-11111-1-111-1-11111111111-1-1-1-11111-111-11-1-1-11-1-11111-1-1-1-1-1-111-1-1-11-11-111-1-11
χ26111111111-1-1-1-1111-1-1-1-11111-1-111-1-11111111111-1-1-1-11111-1-1-1-1111-1111-1-1-1-111-1-1-1-111-1-11-11-11-1-111-1
χ27111111111-1-1-1-1111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111-11-1-1-11-1-1-1-111111111-1-111-111-1-11-111-1
χ28111111111-1-1-1-1111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-111111-1-1-1-11111-1-1111-1-111-11-1-11
χ29111111111-1-1-1-1111-1-1-1-111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1111-11111-111-1-1-1-111-1-111-1-111-1-11-1-111-1-11
χ30111111111-1-1-1-1111-1-1-1-111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11-1-1-11-1-11-1-1-11111-1-1-1-111-1-11111-111-1-111-1
χ31111111111-1-1-1-1111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111111-11111-11111-1-1-1-111-1-111-1-1-1-1-11-11-111-1
χ32111111111-1-1-1-1111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-1-11-1-11-1-1-1-1-1111111-1-111-1-1111-11-11-1-11
χ3322222222-22222-2-2-2-2-222222222-2-222220000000000000000-200-2-200-2-200000000000000000000000000
χ3422222222-22222-2-2-2-2-22222-2-2-2-222-2-2-2-20000000000000000200-2-2002200000000000000000000000000
χ3522222222-22222-2-2-2-2-2-2-2-2-222-2-2-2-222-2-200000000000000002002200-2200000000000000000000000000
χ3622222222-22222-2-2-2-2-2-2-2-2-2-2-22222-2-2220000000000000000-20022002-200000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-20000000000000000-200-22002200000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222220000000000000000200-2200-2-200000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2-2-22200000000000000002002-2002-200000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-222-2-222-2-2222222-2-20000000000000000-2002-200-2200000000000000000000000000
χ4122-2-22-2-2202i2i−2i−2i000002-22i−2i2i−2i2i−2i002-22-2i2i2−i2−i222−2−222−2−2i2i2−i2−i200000000000000000i2−i2i2−i22−22−20000000000
χ4222-2-22-2-2202i2i−2i−2i000002-22i−2i2i−2i2i−2i002-22-2−i2−i2i2i2−2−222−2−222−i2−i2i2i200000000000000000−i2i2−i2i2−22−220000000000
χ4322-2-22-2-2202i2i−2i−2i000002-22i−2i−2i2i−2i2i00-22-22i2i2−i2−i222−2−222−2−2−i2−i2i2i200000000000000000i2−i2−i2i2−22−220000000000
χ4422-2-22-2-2202i2i−2i−2i000002-22i−2i−2i2i−2i2i00-22-22−i2−i2i2i2−2−222−2−222i2i2−i2−i200000000000000000−i2i2i2−i22−22−20000000000
χ4522-2-22-2-2202i2i−2i−2i00000-22−2i2i2i−2i−2i2i002-2-22i2i2−i2−i2−2−22222−2−2−i2−i2i2i200000000000000000−i2i2i2−i22−2−220000000000
χ4622-2-22-2-2202i2i−2i−2i00000-22−2i2i2i−2i−2i2i002-2-22−i2−i2i2i222−2−2−2−222i2i2−i2−i200000000000000000i2−i2−i2i2−222−20000000000
χ4722-2-22-2-2202i2i−2i−2i00000-22−2i2i−2i2i2i−2i00-222-2i2i2−i2−i2−2−22222−2−2i2i2−i2−i200000000000000000−i2i2−i2i2−222−20000000000
χ4822-2-22-2-2202i2i−2i−2i00000-22−2i2i−2i2i2i−2i00-222-2−i2−i2i2i222−2−2−2−222−i2−i2i2i200000000000000000i2−i2i2−i22−2−220000000000
χ4922-2-22-2-220−2i−2i2i2i000002-2−2i2i2i−2i2i−2i00-22-22i2i2−i2−i2−2−222−2−222−i2−i2i2i200000000000000000i2−i2−i2i22−22−20000000000
χ5022-2-22-2-220−2i−2i2i2i000002-2−2i2i2i−2i2i−2i00-22-22−i2−i2i2i222−2−222−2−2i2i2−i2−i200000000000000000−i2i2i2−i2−22−220000000000
χ5122-2-22-2-220−2i−2i2i2i000002-2−2i2i−2i2i−2i2i002-22-2i2i2−i2−i2−2−222−2−222i2i2−i2−i200000000000000000i2−i2i2−i2−22−220000000000
χ5222-2-22-2-220−2i−2i2i2i000002-2−2i2i−2i2i−2i2i002-22-2−i2−i2i2i222−2−222−2−2−i2−i2i2i200000000000000000−i2i2−i2i22−22−20000000000
χ5322-2-22-2-220−2i−2i2i2i00000-222i−2i2i−2i−2i2i00-222-2i2i2−i2−i222−2−2−2−222i2i2−i2−i200000000000000000−i2i2−i2i22−2−220000000000
χ5422-2-22-2-220−2i−2i2i2i00000-222i−2i2i−2i−2i2i00-222-2−i2−i2i2i2−2−22222−2−2−i2−i2i2i200000000000000000i2−i2i2−i2−222−20000000000
χ5522-2-22-2-220−2i−2i2i2i00000-222i−2i−2i2i2i−2i002-2-22i2i2−i2−i222−2−2−2−222−i2−i2i2i200000000000000000−i2i2i2−i2−222−20000000000
χ5622-2-22-2-220−2i−2i2i2i00000-222i−2i−2i2i2i−2i002-2-22−i2−i2i2i2−2−22222−2−2i2i2−i2−i200000000000000000i2−i2−i2i22−2−220000000000
χ572-2-2-2-2222-22-22-22-222-2000000000000002-22-200002-22-200000000000002-22-22-22-2000000000000000000
χ582-2-2-2-2222-22-22-22-222-2000000000000002-22-200002-22-20000000000000-22-22-22-22000000000000000000
χ592-2-2-2-2222-22-22-22-222-200000000000000-22-220000-22-2200000000000002-2-222-2-22000000000000000000
χ602-2-2-2-2222-22-22-22-222-200000000000000-22-220000-22-220000000000000-222-2-222-2000000000000000000
χ612-2-2-2-2222-2-22-222-22-22000000000000002-22-20000-22-2200000000000002-2-22-222-2000000000000000000
χ622-2-2-2-2222-2-22-222-22-22000000000000002-22-20000-22-220000000000000-222-22-2-22000000000000000000
χ632-2-2-2-2222-2-22-222-22-2200000000000000-22-2200002-22-200000000000002-22-2-22-22000000000000000000
χ642-2-2-2-2222-2-22-222-22-2200000000000000-22-2200002-22-20000000000000-22-222-22-2000000000000000000
χ65444-4-44-4-4400004-4-40000000000000000000000000000000004-400000000000000000000000000000000
χ66444-4-44-4-4400004-4-4000000000000000000000000000000000-4400000000000000000000000000000000
χ67444-4-44-4-4-40000-44400000000000000000000000000000000000004i−4i0000000000000000000000000000
χ68444-4-44-4-4-40000-4440000000000000000000000000000000000000−4i4i0000000000000000000000000000
χ694-444-4-4-4404i−4i−4i4i00000000000000000002i2−2i2−2i22i2000022−22−2222000000000000000000000000000000000000000
χ704-444-4-4-4404i−4i−4i4i0000000000000000000−2i22i22i2−2i20000−222222−22000000000000000000000000000000000000000
χ714-444-4-4-440−4i4i4i−4i00000000000000000002i2−2i2−2i22i20000−222222−22000000000000000000000000000000000000000
χ724-444-4-4-440−4i4i4i−4i0000000000000000000−2i22i22i2−2i2000022−22−2222000000000000000000000000000000000000000
χ734-44-44-44-40000000000000000004i−4i000000002i2−2i22i2−2i2000022−2222−2200000000000000000000000000000000000
χ744-44-44-44-40000000000000000004i−4i00000000−2i22i2−2i22i20000−2222−222200000000000000000000000000000000000
χ754-44-44-44-4000000000000000000−4i4i000000002i2−2i22i2−2i20000−2222−222200000000000000000000000000000000000
χ764-44-44-44-4000000000000000000−4i4i00000000−2i22i2−2i22i2000022−2222−2200000000000000000000000000000000000
χ774-4-4444-4-440000-4-44000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ784-4-4444-4-440000-4-4400000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ794-4-4444-4-4-4000044-400000000000000000000000000004i−4i−4i4i00000000000000000000000000000000000
χ804-4-4444-4-4-4000044-40000000000000000000000000000−4i4i4i−4i00000000000000000000000000000000000
χ814-4-4-4-444444-44-4-44-4-4400000000000000000000000000000000000000000000000000000000000000000
χ824-4-4-4-44444-44-44-44-44-400000000000000000000000000000000000000000000000000000000000000000
χ8388-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000

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