Finite Group Databasebeta

← Group #288075

Character table — Group #288075

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888224444444488888888444444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-1-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111111-1-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-11-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-11-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-11-111-1-111-1-1-11
χ172222222222-2-2-222-2000000002222-2-200002222-2-2-2-2000000002200-2-200-2-200000000000000000000
χ182222222222-2-2-222-2000000002222-2-20000-2-2-2-2222200000000-2-200-2-2002200000000000000000000
χ192222222222-2-2-222-200000000-2-2-2-2-2-200002222-2-2-2-200000000-2-20022002200000000000000000000
χ202222222222-2-2-222-200000000-2-2-2-2-2-20000-2-2-2-222220000000022002200-2-200000000000000000000
χ2122222222-2-2222-2-22222222220000-2-2-2-2-2-20000000000000000002200220000000000-2-20000000000
χ2222222222-2-2222-2-22222222220000-2-2-2-2-2-2000000000000000000-2-200-2-20000000000220000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-2-2-20000-2-222220000000000000000002200-2-200000000002-20000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-2-2-20000-2-22222000000000000000000-2-200220000000000-220000000000
χ25222-2-2-2-2200-22200-22i2i2i2i−2i−2i−2i−2i0000000000i2i2−i2−i2i2i2−i2−i22222−2−2−2−2002-2002i−2i0000000000000000i2−i22−200
χ26222-2-2-2-2200-22200-22i2i2i2i−2i−2i−2i−2i0000000000i2i2−i2−i2i2i2−i2−i22222−2−2−2−200-2200−2i2i0000000000000000−i2i2−2200
χ27222-2-2-2-2200-22200-22i2i2i2i−2i−2i−2i−2i0000000000−i2−i2i2i2−i2−i2i2i2−2−2−2−22222002-2002i−2i0000000000000000−i2i2−2200
χ28222-2-2-2-2200-22200-22i2i2i2i−2i−2i−2i−2i0000000000−i2−i2i2i2−i2−i2i2i2−2−2−2−2222200-2200−2i2i0000000000000000i2−i22−200
χ29222-2-2-2-2200-22200-2−2i−2i−2i−2i2i2i2i2i0000000000i2i2−i2−i2i2i2−i2−i2−2−2−2−22222002-200−2i2i0000000000000000i2−i2−2200
χ30222-2-2-2-2200-22200-2−2i−2i−2i−2i2i2i2i2i0000000000i2i2−i2−i2i2i2−i2−i2−2−2−2−2222200-22002i−2i0000000000000000−i2i22−200
χ31222-2-2-2-2200-22200-2−2i−2i−2i−2i2i2i2i2i0000000000−i2−i2i2i2−i2−i2i2i22222−2−2−2−2002-200−2i2i0000000000000000−i2i22−200
χ32222-2-2-2-2200-22200-2−2i−2i−2i−2i2i2i2i2i0000000000−i2−i2i2i2−i2−i2i2i22222−2−2−2−200-22002i−2i0000000000000000i2−i2−2200
χ3322-22-22-2-22-20002-20i2i2−i2−i2i2i2−i2−i222-2-200i2i2−i2−i22-22-20000i2i2−i2−i2i2i2−i2−i22-200000000i2i2−i2−i2i2i2−i2−i2000000000000
χ3422-22-22-2-22-20002-20i2i2−i2−i2i2i2−i2−i222-2-200i2i2−i2−i2-22-220000−i2−i2i2i2−i2−i2i2i2-2200000000i2i2−i2−i2−i2−i2i2i2000000000000
χ3522-22-22-2-22-20002-20i2i2−i2−i2i2i2−i2−i2-2-22200i2i2−i2−i22-22-20000i2i2−i2−i2i2i2−i2−i2-2200000000−i2−i2i2i2−i2−i2i2i2000000000000
χ3622-22-22-2-22-20002-20i2i2−i2−i2i2i2−i2−i2-2-22200i2i2−i2−i2-22-220000−i2−i2i2i2−i2−i2i2i22-200000000−i2−i2i2i2i2i2−i2−i2000000000000
χ3722-22-22-2-22-20002-20−i2−i2i2i2−i2−i2i2i222-2-200−i2−i2i2i22-22-20000−i2−i2i2i2−i2−i2i2i22-200000000−i2−i2i2i2−i2−i2i2i2000000000000
χ3822-22-22-2-22-20002-20−i2−i2i2i2−i2−i2i2i222-2-200−i2−i2i2i2-22-220000i2i2−i2−i2i2i2−i2−i2-2200000000−i2−i2i2i2i2i2−i2−i2000000000000
χ3922-22-22-2-22-20002-20−i2−i2i2i2−i2−i2i2i2-2-22200−i2−i2i2i22-22-20000−i2−i2i2i2−i2−i2i2i2-2200000000i2i2−i2−i2i2i2−i2−i2000000000000
χ4022-22-22-2-22-20002-20−i2−i2i2i2−i2−i2i2i2-2-22200−i2−i2i2i2-22-220000i2i2−i2−i2i2i2−i2−i22-200000000i2i2−i2−i2−i2−i2i2i2000000000000
χ412-22-222-2-22-2000-220i2−i2i2−i2i2−i2i2−i22i−2i2i−2i00i2−i2i2−i200002-22-2i2−i2i2−i2i2−i2i2−i2000000002i−2i2−22−22−22−2000000000000
χ422-22-222-2-22-2000-220i2−i2i2−i2i2−i2i2−i22i−2i2i−2i00i2−i2i2−i20000-22-22−i2i2−i2i2−i2i2−i2i200000000−2i2i2−22−2−22−22000000000000
χ432-22-222-2-22-2000-220i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i00i2−i2i2−i200002-22-2i2−i2i2−i2i2−i2i2−i200000000−2i2i−22−22−22−22000000000000
χ442-22-222-2-22-2000-220i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i00i2−i2i2−i20000-22-22−i2i2−i2i2−i2i2−i2i2000000002i−2i−22−222−22−2000000000000
χ452-22-222-2-22-2000-220−i2i2−i2i2−i2i2−i2i22i−2i2i−2i00−i2i2−i2i200002-22-2−i2i2−i2i2−i2i2−i2i2000000002i−2i−22−22−22−22000000000000
χ462-22-222-2-22-2000-220−i2i2−i2i2−i2i2−i2i22i−2i2i−2i00−i2i2−i2i20000-22-22i2−i2i2−i2i2−i2i2−i200000000−2i2i−22−222−22−2000000000000
χ472-22-222-2-22-2000-220−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i00−i2i2−i2i200002-22-2−i2i2−i2i2−i2i2−i2i200000000−2i2i2−22−22−22−2000000000000
χ482-22-222-2-22-2000-220−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i00−i2i2−i2i20000-22-22i2−i2i2−i2i2−i2i2−i2000000002i−2i2−22−2−22−22000000000000
χ492-2-2-2-2222222-22-2-2-2000000002i−2i−2i2i-220000000000002-2-222-2-2200002i−2i00000000−2i2i2i−2i000000000000
χ502-2-2-2-2222222-22-2-2-2000000002i−2i−2i2i-22000000000000-222-2-222-200002i−2i000000002i−2i−2i2i000000000000
χ512-2-2-2-2222222-22-2-2-200000000−2i2i2i−2i-220000000000002-2-222-2-220000−2i2i000000002i−2i−2i2i000000000000
χ522-2-2-2-2222222-22-2-2-200000000−2i2i2i−2i-22000000000000-222-2-222-20000−2i2i00000000−2i2i2i−2i000000000000
χ532-2-2-2-222222-22-2-2-222-2-222-2-222i−2i−2i2i2-22-2-2200000000000000000000−2i2i0000−2i2i2i−2i0000000000000000
χ542-2-2-2-222222-22-2-2-222-2-222-2-22−2i2i2i−2i2-22-2-22000000000000000000002i−2i00002i−2i−2i2i0000000000000000
χ552-2-2-2-222222-22-2-2-22-222-2-222-22i−2i−2i2i2-2-222-200000000000000000000−2i2i00002i−2i−2i2i0000000000000000
χ562-2-2-2-222222-22-2-2-22-222-2-222-2−2i2i2i−2i2-2-222-2000000000000000000002i−2i0000−2i2i2i−2i0000000000000000
χ572-2-2-2-2222-2-2-22-22222-2-222-2-220000-22-222-20000000000000000000000000000000000002-22-2000000
χ582-2-2-2-2222-2-2-22-22222-2-222-2-220000-22-222-2000000000000000000000000000000000000-22-22000000
χ592-2-2-2-2222-2-2-22-2222-222-2-222-20000-222-2-220000000000000000000000000000000000002-2-22000000
χ602-2-2-2-2222-2-2-22-2222-222-2-222-20000-222-2-22000000000000000000000000000000000000-222-2000000
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ62444-4-4-4-44004-4-40040000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ63444-4-4-4-44004-4-4004000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ6444-44-44-4-4-44000-4402i22i2−2i2−2i22i22i2−2i2−2i2000000−2i2−2i22i22i20000000000000000000000000000000000000000000000
χ6544-44-44-4-4-44000-440−2i2−2i22i22i2−2i2−2i22i22i20000002i22i2−2i2−2i20000000000000000000000000000000000000000000000
χ6644-4-44-44-4000000002222−22−22−22−22222200000000002i2−2i2−2i22i20000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6744-4-44-44-4000000002222−22−22−22−2222220000000000−2i22i22i2−2i200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6844-4-44-44-400000000−22−2222222222−22−2200000000002i2−2i2−2i22i200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6944-4-44-44-400000000−22−2222222222−22−220000000000−2i22i22i2−2i20000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ704-444-4-44-40000000022−2222−22−2222−2222000000000000002i2−2i2−2i22i2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ714-444-4-44-40000000022−2222−22−2222−222200000000000000−2i22i22i2−2i22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ724-444-4-44-400000000−2222−222222−2222−22000000000000002i2−2i2−2i22i22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ734-444-4-44-400000000−2222−222222−2222−2200000000000000−2i22i22i2−2i2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ744-44-444-4-4-440004-402i2−2i22i2−2i22i2−2i22i2−2i2000000−2i22i2−2i22i20000000000000000000000000000000000000000000000
χ754-44-444-4-4-440004-40−2i22i2−2i22i2−2i22i2−2i22i20000002i2−2i22i2−2i20000000000000000000000000000000000000000000000
χ764-4-444-4-440044-400-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ774-4-444-4-440044-400-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ784-4-444-4-4400-4-440040000000000000000000000000022−22−2222−222222−22000000000000000000000000000000
χ794-4-444-4-4400-4-4400400000000000000000000000000−222222−2222−22−2222000000000000000000000000000000
χ804-4-4-4-4444-4-44-4444-40000000000004-400000000000000000000000000000000000000000000000000

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