Finite Group Databasebeta

← Group #229346

Character table — Group #229346

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444444444444444444488888888888844444444448888888888888888884444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ711111111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111
χ811111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ91111111111111111-1-1-1-11111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111
χ111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111
χ121111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1111111-1-1-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ1711-1-1-111-1-111-1-1-111ii−i−iii−i−i1ii−i−i-111-1-1iiii−i−i−i−ii−ii−i11-1-1i−iii−i−i1-111-1-111-1-1ii−i−i1-11-1i−ii−i1-1
χ1811-1-1-111-1-111-1-1-111ii−i−iii−i−i1ii−i−i-111-1-1−i−i−i−iiiiii−ii−i-1-111i−iii−i−i1-1-1-111-1-111−i−iii1-11-1−ii−ii-11
χ1911-1-1-111-1-111-1-1-111ii−i−iii−i−i1−i−iii-111-1-1iiii−i−i−i−ii−i−ii-1-111i−i−i−iii1-111-1-111-1-1ii−i−i-11-11−ii−ii-11
χ2011-1-1-111-1-111-1-1-111ii−i−iii−i−i1−i−iii-111-1-1−i−i−i−iiiiii−i−ii11-1-1i−i−i−iii1-1-1-111-1-111−i−iii-11-11i−ii−i1-1
χ2111-1-1-111-1-111-1-1-111ii−i−i−i−iii1ii−i−i-1-1-111iiii−i−i−i−ii−ii−i11-1-1−ii−i−iii-1111-1-1-1-111−i−iii1-1-11i−i−ii-11
χ2211-1-1-111-1-111-1-1-111ii−i−i−i−iii1ii−i−i-1-1-111−i−i−i−iiiiii−ii−i-1-111−ii−i−iii-11-1-11111-1-1ii−i−i1-1-11−iii−i1-1
χ2311-1-1-111-1-111-1-1-111ii−i−i−i−iii1−i−iii-1-1-111iiii−i−i−i−ii−i−ii-1-111−iiii−i−i-1111-1-1-1-111−i−iii-111-1−iii−i1-1
χ2411-1-1-111-1-111-1-1-111ii−i−i−i−iii1−i−iii-1-1-111−i−i−i−iiiiii−i−ii11-1-1−iiii−i−i-11-1-11111-1-1ii−i−i-111-1i−i−ii-11
χ2511-1-1-111-1-111-1-1-111−i−iiiii−i−i1ii−i−i-1-1-111iiii−i−i−i−i−iii−i11-1-1i−i−i−iii-11-1-11111-1-1−i−iii-111-1−iii−i-11
χ2611-1-1-111-1-111-1-1-111−i−iiiii−i−i1ii−i−i-1-1-111−i−i−i−iiiii−iii−i-1-111i−i−i−iii-1111-1-1-1-111ii−i−i-111-1i−i−ii1-1
χ2711-1-1-111-1-111-1-1-111−i−iiiii−i−i1−i−iii-1-1-111iiii−i−i−i−i−ii−ii-1-111i−iii−i−i-11-1-11111-1-1−i−iii1-1-11i−i−ii1-1
χ2811-1-1-111-1-111-1-1-111−i−iiiii−i−i1−i−iii-1-1-111−i−i−i−iiiii−ii−ii11-1-1i−iii−i−i-1111-1-1-1-111ii−i−i1-1-11−iii−i-11
χ2911-1-1-111-1-111-1-1-111−i−iii−i−iii1ii−i−i-111-1-1iiii−i−i−i−i−iii−i11-1-1−iiii−i−i1-1-1-111-1-111ii−i−i-11-11−ii−ii1-1
χ3011-1-1-111-1-111-1-1-111−i−iii−i−iii1ii−i−i-111-1-1−i−i−i−iiiii−iii−i-1-111−iiii−i−i1-111-1-111-1-1−i−iii-11-11i−ii−i-11
χ3111-1-1-111-1-111-1-1-111−i−iii−i−iii1−i−iii-111-1-1iiii−i−i−i−i−ii−ii-1-111−ii−i−iii1-1-1-111-1-111ii−i−i1-11-1i−ii−i-11
χ3211-1-1-111-1-111-1-1-111−i−iii−i−iii1−i−iii-111-1-1−i−i−i−iiiii−ii−ii11-1-1−ii−i−iii1-111-1-111-1-1−i−iii1-11-1−ii−ii1-1
χ33222222222-22-2-222-222222222-20000-2222200000000-2-2000000-2-20000-2-20000000000000000000000
χ34222222222-22-2-222-22222-2-2-2-2-20000-2-2-2-2-200000000-2-2000000220000220000000000000000000000
χ35222222222-22-2-222-2-2-2-2-22222-20000-2-2-2-2-20000000022000000-2-20000220000000000000000000000
χ36222222222-22-2-222-2-2-2-2-2-2-2-2-2-20000-222220000000022000000220000-2-20000000000000000000000
χ3722222222-22-222-2-2200000000-22222-2000022-2-222-2-200-2-22-22-2000000000000000000000000000000
χ3822222222-22-222-2-2200000000-22222-20000-2-222-2-22200-2-2-22-22000000000000000000000000000000
χ3922222222-22-222-2-2200000000-2-2-2-2-2-2000022-2-222-2-20022-22-22000000000000000000000000000000
χ4022222222-22-222-2-2200000000-2-2-2-2-2-20000-2-222-2-22200222-22-2000000000000000000000000000000
χ412222-2-2-2-220200-2-202-22-22-22-20000002-22-22−22−22−22−200000000000000002−22−22−22−22−22−20000000000
χ422222-2-2-2-220200-2-202-22-22-22-20000002-22-2−22−22−22−220000000000000000−22−22−22−22−22−220000000000
χ432222-2-2-2-220200-2-202-22-2-22-22000000-22-222−22−22−22−200000000000000002−22−2−22−22−22−220000000000
χ442222-2-2-2-220200-2-202-22-2-22-22000000-22-22−22−22−22−220000000000000000−22−222−22−22−22−20000000000
χ452222-2-2-2-220200-2-20-22-222-22-2000000-22-222−22−22−22−20000000000000000−22−222−22−2−22−220000000000
χ462222-2-2-2-220200-2-20-22-222-22-2000000-22-22−22−22−22−2200000000000000002−22−2−22−222−22−20000000000
χ472222-2-2-2-220200-2-20-22-22-22-220000002-22-22−22−22−22−20000000000000000−22−22−22−222−22−20000000000
χ482222-2-2-2-220200-2-20-22-22-22-220000002-22-2−22−22−22−2200000000000000002−22−22−22−2−22−220000000000
χ4922-2-22-2-22-202002-202i−2i−2i2i2i−2i−2i2i0000002-2-22i2−i2i2−i2−i2i2−i2i200000000000000002−2−222−2−22i2−i2−i2i20000000000
χ5022-2-22-2-22-202002-202i−2i−2i2i2i−2i−2i2i0000002-2-22−i2i2−i2i2i2−i2i2−i20000000000000000−222−2−222−2−i2i2i2−i20000000000
χ5122-2-22-2-22-202002-202i−2i−2i2i−2i2i2i−2i000000-222-2i2−i2i2−i2−i2i2−i2i200000000000000002−2−22−222−2−i2i2i2−i20000000000
χ5222-2-22-2-22-202002-202i−2i−2i2i−2i2i2i−2i000000-222-2−i2i2−i2i2i2−i2i2−i20000000000000000−222−22−2−22i2−i2−i2i20000000000
χ5322-2-22-2-22-202002-20−2i2i2i−2i2i−2i−2i2i000000-222-2i2−i2i2−i2−i2i2−i2i20000000000000000−222−22−2−22−i2i2i2−i20000000000
χ5422-2-22-2-22-202002-20−2i2i2i−2i2i−2i−2i2i000000-222-2−i2i2−i2i2i2−i2i2−i200000000000000002−2−22−222−2i2−i2−i2i20000000000
χ5522-2-22-2-22-202002-20−2i2i2i−2i−2i2i2i−2i0000002-2-22i2−i2i2−i2−i2i2−i2i20000000000000000−222−2−222−2i2−i2−i2i20000000000
χ5622-2-22-2-22-202002-20−2i2i2i−2i−2i2i2i−2i0000002-2-22−i2i2−i2i2i2−i2i2−i200000000000000002−2−222−2−22−i2i2i2−i20000000000
χ5722-2-2-222-222-2-2-22-2200000000-22i2i−2i−2i200002i2i−2i−2i−2i−2i2i2i00−2i2i2-2-22000000000000000000000000000000
χ5822-2-2-222-222-2-2-22-2200000000-22i2i−2i−2i20000−2i−2i2i2i2i2i−2i−2i00−2i2i-222-2000000000000000000000000000000
χ5922-2-2-222-222-2-2-22-2200000000-2−2i−2i2i2i200002i2i−2i−2i−2i−2i2i2i002i−2i-222-2000000000000000000000000000000
χ6022-2-2-222-222-2-2-22-2200000000-2−2i−2i2i2i20000−2i−2i2i2i2i2i−2i−2i002i−2i2-2-22000000000000000000000000000000
χ6122-2-2-222-2-2-2222-22-22i2i−2i−2i2i2i−2i−2i-20000222-2-200000000−2i2i000000−2i2i0000-220000000000000000000000
χ6222-2-2-222-2-2-2222-22-22i2i−2i−2i−2i−2i2i2i-200002-2-22200000000−2i2i0000002i−2i00002-20000000000000000000000
χ6322-2-2-222-2-2-2222-22-2−2i−2i2i2i2i2i−2i−2i-200002-2-222000000002i−2i000000−2i2i00002-20000000000000000000000
χ6422-2-2-222-2-2-2222-22-2−2i−2i2i2i−2i−2i2i2i-20000222-2-2000000002i−2i0000002i−2i0000-220000000000000000000000
χ6544444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ664444-4-4-4-4-40-40044000000000000000000022−22−222222−22−222200000000000000000000000000000000000000
χ674444-4-4-4-4-40-400440000000000000000000−222222−22−222222−2200000000000000000000000000000000000000
χ6844-4-44-4-4440-400-4400000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ6944-4-44-4-4440-400-440000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ7044-4-4-444-44-4-4444-4-40000000040000-400000000000000000000000000000000000000000000000000
χ714-44-444-4-40404-400-400000000000000000000000000000000000022−2222−22000000000000000000000000
χ724-44-444-4-40404-400-4000000000000000000000000000000000000−2222−2222000000000000000000000000
χ734-44-444-4-40-40-440040000000004i−4i4i−4i000000000000000000000000000000000000000000000000000
χ744-44-444-4-40-40-44004000000000−4i4i−4i4i000000000000000000000000000000000000000000000000000
χ754-4-44-44-44040-4400-40000000000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ764-4-44-44-44040-4400-4000000000000000000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ774-4-44-44-440-404-40040000000004-4-44000000000000000000000000000000000000000000000000000
χ784-4-44-44-440-404-4004000000000-444-4000000000000000000000000000000000000000000000000000
χ798-88-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-888-88-8000000000000000000000000000000000000000000000000000000000000000000000000

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