Finite Group Databasebeta

← Group #229375

Character table — Group #229375

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888844444444448888888888888888888844444444444488888888222244448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-111-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111
χ51111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111-1-111-1-1-1-1
χ61111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1
χ121111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-111
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1111111-1-1
χ1711-111-1-1-1-11-1-1-1111iiii−i−i−i−i1ii−i−iii−i−i-1ii−i−i11-1-111-1-1iiii−i−i−i−ii−i11-1-1ii−i−ii−i11-1-111-1-11-11-1i−ii−ii−i1-1
χ1811-111-1-1-1-11-1-1-1111iiii−i−i−i−i1ii−i−iii−i−i-1ii−i−i11-1-111-1-1iiii−i−i−i−ii−i-1-111−i−iiii−i11-1-111-1-1-11-11−ii−ii−ii-11
χ1911-111-1-1-1-11-1-1-1111iiii−i−i−i−i1ii−i−i−i−iii-1ii−i−i-1-111-1-111−i−i−i−iiiiii−i11-1-1ii−i−i−ii11-1-1-1-1111-1-11i−i−ii−ii-11
χ2011-111-1-1-1-11-1-1-1111iiii−i−i−i−i1ii−i−i−i−iii-1ii−i−i-1-111-1-111−i−i−i−iiiiii−i-1-111−i−iii−ii11-1-1-1-111-111-1−iii−ii−i1-1
χ2111-111-1-1-1-11-1-1-1111iiii−i−i−i−i1−i−iiiii−i−i-1ii−i−i-1-111-1-111−i−i−i−iiiii−ii11-1-1ii−i−ii−i-1-11111-1-1-111-1−iii−i−ii-11
χ2211-111-1-1-1-11-1-1-1111iiii−i−i−i−i1−i−iiiii−i−i-1ii−i−i-1-111-1-111−i−i−i−iiiii−ii-1-111−i−iiii−i-1-11111-1-11-1-11i−i−iii−i1-1
χ2311-111-1-1-1-11-1-1-1111iiii−i−i−i−i1−i−iii−i−iii-1ii−i−i11-1-111-1-1iiii−i−i−i−i−ii11-1-1ii−i−i−ii-1-111-1-111-11-11−ii−iii−i1-1
χ2411-111-1-1-1-11-1-1-1111iiii−i−i−i−i1−i−iii−i−iii-1ii−i−i11-1-111-1-1iiii−i−i−i−i−ii-1-111−i−iii−ii-1-111-1-1111-11-1i−ii−i−ii-11
χ2511-111-1-1-1-11-1-1-1111−i−i−i−iiiii1ii−i−iii−i−i-1−i−iii11-1-111-1-1−i−i−i−iiiiii−i11-1-1−i−iiii−i-1-111-1-111-11-11i−ii−i−ii1-1
χ2611-111-1-1-1-11-1-1-1111−i−i−i−iiiii1ii−i−iii−i−i-1−i−iii11-1-111-1-1−i−i−i−iiiiii−i-1-111ii−i−ii−i-1-111-1-1111-11-1−ii−iii−i-11
χ2711-111-1-1-1-11-1-1-1111−i−i−i−iiiii1ii−i−i−i−iii-1−i−iii-1-111-1-111iiii−i−i−i−ii−i11-1-1−i−iii−ii-1-11111-1-1-111-1i−i−iii−i-11
χ2811-111-1-1-1-11-1-1-1111−i−i−i−iiiii1ii−i−i−i−iii-1−i−iii-1-111-1-111iiii−i−i−i−ii−i-1-111ii−i−i−ii-1-11111-1-11-1-11−iii−i−ii1-1
χ2911-111-1-1-1-11-1-1-1111−i−i−i−iiiii1−i−iiiii−i−i-1−i−iii-1-111-1-111iiii−i−i−i−i−ii11-1-1−i−iiii−i11-1-1-1-1111-1-11−iii−ii−i-11
χ3011-111-1-1-1-11-1-1-1111−i−i−i−iiiii1−i−iiiii−i−i-1−i−iii-1-111-1-111iiii−i−i−i−i−ii-1-111ii−i−ii−i11-1-1-1-111-111-1i−i−ii−ii1-1
χ3111-111-1-1-1-11-1-1-1111−i−i−i−iiiii1−i−iii−i−iii-1−i−iii11-1-111-1-1−i−i−i−iiiii−ii11-1-1−i−iii−ii11-1-111-1-11-11-1−ii−ii−ii1-1
χ3211-111-1-1-1-11-1-1-1111−i−i−i−iiiii1−i−iii−i−iii-1−i−iii11-1-111-1-1−i−i−i−iiiii−ii-1-111ii−i−i−ii11-1-111-1-1-11-11i−ii−ii−i-11
χ332222222222-2-22-2-2200000000-222222222-200002222-2-2-2-200000000-2-200000000-2-200000000000000000000
χ342222222222-2-22-2-2200000000-22222-2-2-2-2-20000-2-2-2-2222200000000-2-2000000002200000000000000000000
χ352222222222-2-22-2-2200000000-2-2-2-2-22222-20000-2-2-2-22222000000002200000000-2-200000000000000000000
χ362222222222-2-22-2-2200000000-2-2-2-2-2-2-2-2-2-200002222-2-2-2-20000000022000000002200000000000000000000
χ3722222222-2-222-222-222222222-200000000-2-2-2-2-20000000000000000002-22-22-22-20000000000000000000000
χ3822222222-2-222-222-222222222-200000000-2-2-2-2-2000000000000000000-22-22-22-220000000000000000000000
χ3922222222-2-222-222-2-2-2-2-2-2-2-2-2-200000000-222220000000000000000002-22-2-22-220000000000000000000000
χ4022222222-2-222-222-2-2-2-2-2-2-2-2-2-200000000-22222000000000000000000-22-222-22-20000000000000000000000
χ41222-2-2-2-222200-200-222−2−222−2−202i−2i2i−2i2i−2i2i−2i02−22−22-22-2000022−2−222−2−2000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ42222-2-2-2-222200-200-222−2−222−2−202i−2i2i−2i−2i2i−2i2i02−22−2-22-220000−2−222−2−222000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ43222-2-2-2-222200-200-222−2−222−2−20−2i2i−2i2i2i−2i2i−2i02−22−2-22-220000−2−222−2−222000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ44222-2-2-2-222200-200-222−2−222−2−20−2i2i−2i2i−2i2i−2i2i02−22−22-22-2000022−2−222−2−2000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ45222-2-2-2-222200-200-2−2−222−2−22202i−2i2i−2i2i−2i2i−2i0−22−222-22-20000−2−222−2−222000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ46222-2-2-2-222200-200-2−2−222−2−22202i−2i2i−2i−2i2i−2i2i0−22−22-22-22000022−2−222−2−2000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ47222-2-2-2-222200-200-2−2−222−2−2220−2i2i−2i2i2i−2i2i−2i0−22−22-22-22000022−2−222−2−2000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ48222-2-2-2-222200-200-2−2−222−2−2220−2i2i−2i2i−2i2i−2i2i0−22−222-22-20000−2−222−2−222000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ4922-222-2-2-22-2-2-2222-22i2i2i2i−2i−2i−2i−2i-2000000002−2i−2i2i2i0000000000000000002-2-222i−2i−2i2i0000000000000000000000
χ5022-222-2-2-22-2-2-2222-22i2i2i2i−2i−2i−2i−2i-2000000002−2i−2i2i2i000000000000000000-222-2−2i2i2i−2i0000000000000000000000
χ5122-222-2-2-22-2-2-2222-2−2i−2i−2i−2i2i2i2i2i-20000000022i2i−2i−2i0000000000000000002-2-22−2i2i2i−2i0000000000000000000000
χ5222-222-2-2-22-2-2-2222-2−2i−2i−2i−2i2i2i2i2i-20000000022i2i−2i−2i000000000000000000-222-22i−2i−2i2i0000000000000000000000
χ5322-222-2-2-2-2222-2-2-2200000000-22i2i−2i−2i2i2i−2i−2i2000022-2-2-2-22200000000−2i2i00000000−2i2i00000000000000000000
χ5422-222-2-2-2-2222-2-2-2200000000-22i2i−2i−2i−2i−2i2i2i20000-2-22222-2-200000000−2i2i000000002i−2i00000000000000000000
χ5522-222-2-2-2-2222-2-2-2200000000-2−2i−2i2i2i2i2i−2i−2i20000-2-22222-2-2000000002i−2i00000000−2i2i00000000000000000000
χ5622-222-2-2-2-2222-2-2-2200000000-2−2i−2i2i2i−2i−2i2i2i2000022-2-2-2-222000000002i−2i000000002i−2i00000000000000000000
χ5722-2-2-222-2-2200200-2i2i2−i2−i2−i2−i2i2i202-2-222-2-220i2−i2−i2i22-2-220000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ5822-2-2-222-2-2200200-2i2i2−i2−i2−i2−i2i2i202-2-22-222-20i2−i2−i2i2-222-20000−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ5922-2-2-222-2-2200200-2i2i2−i2−i2−i2−i2i2i20-222-22-2-220i2−i2−i2i2-222-20000−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ6022-2-2-222-2-2200200-2i2i2−i2−i2−i2−i2i2i20-222-2-222-20i2−i2−i2i22-2-220000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ6122-2-2-222-2-2200200-2−i2−i2i2i2i2i2−i2−i202-2-222-2-220−i2i2i2−i22-2-220000−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ6222-2-2-222-2-2200200-2−i2−i2i2i2i2i2−i2−i202-2-22-222-20−i2i2i2−i2-222-20000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ6322-2-2-222-2-2200200-2−i2−i2i2i2i2i2−i2−i20-222-22-2-220−i2i2i2−i2-222-20000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ6422-2-2-222-2-2200200-2−i2−i2i2i2i2i2−i2−i20-222-2-222-20−i2i2i2−i22-2-220000−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ6544444444-4-4-4-4-4-4-4-40000000040000000040000000000000000000000000000000000000000000000000000
χ66444-4-4-4-44-4-40040042222−22−222222−22−220000000000−2222−2222000000000000000000000000000000000000000000000000
χ67444-4-4-4-44-4-4004004−22−222222−22−222222000000000022−2222−22000000000000000000000000000000000000000000000000
χ6844-444-4-4-44-4444-4-4-400000000400000000-40000000000000000000000000000000000000000000000000000
χ6944-4-4-444-44-400-40042i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ7044-4-4-444-44-400-4004−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ714-444-44-4-4000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000022−2222−222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ724-444-44-4-4000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000−2222−2222−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ734-444-44-4-400000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000022−2222−22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ744-444-44-4-400000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000−2222−22222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ754-44-44-44-4004-404-400000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000
χ764-44-44-44-4004-404-40000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000
χ774-44-44-44-400-440-4404i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ784-44-44-44-400-440-440−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ794-4-44-4-4440000000022−2222−22−2222−222200000000000000000022−22−22222-22-2-22-2200000000000000000000000000000000
χ804-4-44-4-4440000000022−2222−22−2222−2222000000000000000000−222222−22-22-222-22-200000000000000000000000000000000
χ814-4-44-4-44400000000−2222−222222−2222−2200000000000000000022−22−2222-22-222-22-200000000000000000000000000000000
χ824-4-44-4-44400000000−2222−222222−2222−22000000000000000000−222222−222-22-2-22-2200000000000000000000000000000000
χ834-4-4-444-44004-40-4404-4-44-444-400000000000000000000000000000000000000000000000000000000000000
χ844-4-4-444-44004-40-440-444-44-4-4400000000000000000000000000000000000000000000000000000000000000
χ854-4-4-444-4400-4404-4000000000000000000000000000000022−22−2222−222222−2200000000000000000000000000000000
χ864-4-4-444-4400-4404-40000000000000000000000000000000−222222−2222−22−222200000000000000000000000000000000

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