Finite Group Databasebeta

← Group #288104

Character table — Group #288104

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888224444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ7111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1111-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111111-1-1-111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-11-1-111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11-111-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111111111-1-1-1-111-11-1-1-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-11-11111-1-1-11
χ17222222222-2-22-222-2222222220000-2-20000-2-2-2-200000000000000222200000000000000-2-200000000
χ18222222222-2-22-222-2222222220000-2-20000-2-2-2-200000000000000-2-2-2-2000000000000002200000000
χ19222222222-2-22-222-2-2-2-2-2-2-2-2-20000-2-2000022220000000000000022-2-2000000000000002-200000000
χ20222222222-2-22-222-2-2-2-2-2-2-2-2-20000-2-20000222200000000000000-2-22200000000000000-2200000000
χ2122222222-222-22-2-22000000002222-2-222220000-2-2-2-200000000-2-2000022-2-200000000000000000000
χ2222222222-222-22-2-22000000002222-2-2-2-2-2-20000222200000000-2-20000-2-22200000000000000000000
χ2322222222-222-22-2-2200000000-2-2-2-2-2-222220000-2-2-2-200000000220000-2-22200000000000000000000
χ2422222222-222-22-2-2200000000-2-2-2-2-2-2-2-2-2-2000022220000000022000022-2-200000000000000000000
χ25222-2-2-22-202-20-20022222−2−2−2−22i2i−2i−2i002i2i−2i−2i22−2−20000i2i2i2i2−i2−i2−i2−i20000002-200i2i2−i2−i222−2−2000000000000
χ26222-2-2-22-202-20-20022222−2−2−2−22i2i−2i−2i00−2i−2i2i2i22−2−20000−i2−i2−i2−i2i2i2i2i2000000-2200i2i2−i2−i2−2−222000000000000
χ27222-2-2-22-202-20-20022222−2−2−2−2−2i−2i2i2i002i2i−2i−2i22−2−20000i2i2i2i2−i2−i2−i2−i2000000-2200−i2−i2i2i2−2−222000000000000
χ28222-2-2-22-202-20-20022222−2−2−2−2−2i−2i2i2i00−2i−2i2i2i22−2−20000−i2−i2−i2−i2i2i2i2i20000002-200−i2−i2i2i222−2−2000000000000
χ29222-2-2-22-202-20-2002−2−2−2−222222i2i−2i−2i002i2i−2i−2i−2−2220000−i2−i2−i2−i2i2i2i2i20000002-200−i2−i2i2i2−2−222000000000000
χ30222-2-2-22-202-20-2002−2−2−2−222222i2i−2i−2i00−2i−2i2i2i−2−2220000i2i2i2i2−i2−i2−i2−i2000000-2200−i2−i2i2i222−2−2000000000000
χ31222-2-2-22-202-20-2002−2−2−2−22222−2i−2i2i2i002i2i−2i−2i−2−2220000−i2−i2−i2−i2i2i2i2i2000000-2200i2i2−i2−i222−2−2000000000000
χ32222-2-2-22-202-20-2002−2−2−2−22222−2i−2i2i2i00−2i−2i2i2i−2−2220000i2i2i2i2−i2−i2−i2−i20000002-200i2i2−i2−i2−2−222000000000000
χ332-22-222-2-2200-20-2202i2i−2i−2i2i2i−2i−2i000000i2−i2i2−i20000i2i2−i2−i222−2−222−2−2002i−2i2-20000000000000000002−2i2−i200
χ342-22-222-2-2200-20-2202i2i−2i−2i2i2i−2i−2i000000i2−i2i2−i20000i2i2−i2−i222−2−222−2−200−2i2i-22000000000000000000−22−i2i200
χ352-22-222-2-2200-20-2202i2i−2i−2i2i2i−2i−2i000000−i2i2−i2i20000−i2−i2i2i2−2−222−2−222002i−2i2-2000000000000000000−22−i2i200
χ362-22-222-2-2200-20-2202i2i−2i−2i2i2i−2i−2i000000−i2i2−i2i20000−i2−i2i2i2−2−222−2−22200−2i2i-220000000000000000002−2i2−i200
χ372-22-222-2-2200-20-220−2i−2i2i2i−2i−2i2i2i000000i2−i2i2−i20000i2i2−i2−i2−2−222−2−222002i−2i-220000000000000000002−2−i2i200
χ382-22-222-2-2200-20-220−2i−2i2i2i−2i−2i2i2i000000i2−i2i2−i20000i2i2−i2−i2−2−222−2−22200−2i2i2-2000000000000000000−22i2−i200
χ392-22-222-2-2200-20-220−2i−2i2i2i−2i−2i2i2i000000−i2i2−i2i20000−i2−i2i2i222−2−222−2−2002i−2i-22000000000000000000−22i2−i200
χ402-22-222-2-2200-20-220−2i−2i2i2i−2i−2i2i2i000000−i2i2−i2i20000−i2−i2i2i222−2−222−2−200−2i2i2-20000000000000000002−2−i2i200
χ412-2-22-222-202-20200-22−22−22−22−22-22-20000002−22−22i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000000002i−2i2−22−2i2−i2i2−i2000000000000
χ422-2-22-222-202-20200-22−22−22−22−22-22-20000002−22−2−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200000000−2i2i2−22−2−i2i2−i2i2000000000000
χ432-2-22-222-202-20200-22−22−22−22−2-22-220000002−22−22i−2i2i−2ii2−i2i2−i2i2−i2i2−i200000000−2i2i−22−22−i2i2−i2i2000000000000
χ442-2-22-222-202-20200-22−22−22−22−2-22-220000002−22−2−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000000002i−2i−22−22i2−i2i2−i2000000000000
χ452-2-22-222-202-20200-2−22−22−22−222-22-2000000−22−222i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000002i−2i−22−22−i2i2−i2i2000000000000
χ462-2-22-222-202-20200-2−22−22−22−222-22-2000000−22−22−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200000000−2i2i−22−22i2−i2i2−i2000000000000
χ472-2-22-222-202-20200-2−22−22−22−22-22-22000000−22−222i−2i2i−2i−i2i2−i2i2−i2i2−i2i200000000−2i2i2−22−2i2−i2i2−i2000000000000
χ482-2-22-222-202-20200-2−22−22−22−22-22-22000000−22−22−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000002i−2i2−22−2−i2i2−i2i2000000000000
χ492-2-2-22-222222-2-22-2-2000000002i−2i−2i2i-220000000000002-22-2-22-222i−2i000000000000−2i2i2i−2i000000000000
χ502-2-2-22-222222-2-22-2-2000000002i−2i−2i2i-22000000000000-22-222-22-22i−2i0000000000002i−2i−2i2i000000000000
χ512-2-2-22-222222-2-22-2-200000000−2i2i2i−2i-220000000000002-22-2-22-22−2i2i0000000000002i−2i−2i2i000000000000
χ522-2-2-22-222222-2-22-2-200000000−2i2i2i−2i-22000000000000-22-222-22-2−2i2i000000000000−2i2i2i−2i000000000000
χ532-2-2-22-222-2222-2-22-22-22-2-22-222i−2i−2i2i2-200002-2-22000000000000−2i2i000000002i−2i−2i2i0000000000000000
χ542-2-2-22-222-2222-2-22-22-22-2-22-22−2i2i2i−2i2-200002-2-220000000000002i−2i00000000−2i2i2i−2i0000000000000000
χ552-2-2-22-222-2222-2-22-2-22-222-22-22i−2i−2i2i2-20000-222-2000000000000−2i2i00000000−2i2i2i−2i0000000000000000
χ562-2-2-22-222-2222-2-22-2-22-222-22-2−2i2i2i−2i2-20000-222-20000000000002i−2i000000002i−2i−2i2i0000000000000000
χ572-2-2-22-222-2-2-222-2222-22-2-22-220000-220000-222-20000000000000000000000000000002-2002-2000000
χ582-2-2-22-222-2-2-222-2222-22-2-22-220000-220000-222-2000000000000000000000000000000-2200-22000000
χ592-2-2-22-222-2-2-222-222-22-222-22-20000-2200002-2-220000000000000000000000000000002-200-22000000
χ602-2-2-22-222-2-2-222-222-22-222-22-20000-2200002-2-22000000000000000000000000000000-22002-2000000
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ62444-4-4-44-40-440400-422222222−22−22−22−220000000000−22−222222000000000000000000000000000000000000000000
χ63444-4-4-44-40-440400-4−22−22−22−222222222200000000002222−22−22000000000000000000000000000000000000000000
χ6444-444-4-4-440040-4-400000000000000000000000000022−22−2222−222222−22000000000000000000000000000000
χ6544-444-4-4-440040-4-4000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000
χ6644-444-4-4-4-400-404404i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ6744-444-4-4-4-400-40440−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ6844-4-4-44-44000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000022−22−2222−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ6944-4-4-44-44000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000−222222−222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ7044-4-4-44-4400000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000022−22−22222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ7144-4-4-44-4400000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000−222222−22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ724-444-4-4-44000000002i22i2−2i2−2i2−2i2−2i22i22i200000022−22−222200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ734-444-4-4-44000000002i22i2−2i2−2i2−2i2−2i22i22i2000000−222222−22000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ744-444-4-4-4400000000−2i2−2i22i22i22i22i2−2i2−2i200000022−22−2222000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ754-444-4-4-4400000000−2i2−2i22i22i22i22i2−2i2−2i2000000−222222−2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ764-44-444-4-4-400404-40000000000000002i2−2i22i2−2i20000−2i2−2i22i22i200000000000000000000000000000000000000
χ774-44-444-4-4-400404-4000000000000000−2i22i2−2i22i200002i22i2−2i2−2i200000000000000000000000000000000000000
χ784-4-44-444-40-440-400422−2222−2222−2222−220000000000−2222−2222000000000000000000000000000000000000000000
χ794-4-44-444-40-440-4004−2222−2222−2222−2222000000000022−2222−22000000000000000000000000000000000000000000
χ804-4-4-44-4444-4-4-444-440000000000004-400000000000000000000000000000000000000000000000000

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