Finite Group Databasebeta

← Group #225544

Character table — Group #225544

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888844444444448888888888888888888822224444444488888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-111
χ171111-1-1-1-1-1-1111-1-111111-1-1-1-1-111-1-111-1-1111-1-11111-1-1-1-11111-1-1-1-11-11-1ii−i−iii−i−i11-1-111-1-1i−ii−ii−ii−ii−ii−i
χ181111-1-1-1-1-1-1111-1-111111-1-1-1-1-111-1-111-1-1111-1-11111-1-1-1-11111-1-1-1-11-11-1−i−iii−i−iii11-1-111-1-1−ii−ii−ii−ii−ii−ii
χ191111-1-1-1-1-1-1111-1-111111-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-111111-1-11ii−i−iii−i−i11-1-1-1-111i−ii−i−ii−ii−ii−ii
χ201111-1-1-1-1-1-1111-1-111111-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-111111-1-11−i−iii−i−iii11-1-1-1-111−ii−iii−ii−ii−ii−i
χ211111-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1-11111-1-1111-1-1-1-1-1-11111-1-1-1-11111-111-1ii−i−iii−i−i-1-11111-1-1−ii−iii−ii−i−ii−ii
χ221111-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1-11111-1-1111-1-1-1-1-1-11111-1-1-1-11111-111-1−i−iii−i−iii-1-11111-1-1i−ii−i−ii−iii−ii−i
χ231111-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1-111-1-111111-1-11111-1-1-1-11111-1-1-1-1-11-11ii−i−iii−i−i-1-111-1-111−ii−ii−ii−iii−ii−i
χ241111-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1-111-1-111111-1-11111-1-1-1-11111-1-1-1-1-11-11−i−iii−i−iii-1-111-1-111i−ii−ii−ii−i−ii−ii
χ251111-1-1-1-1-1-1111-1-11-1-1-1-11111-111-1-111-1-11-1-1111111-1-1-1-1-1-1-1-111111-11-1ii−i−i−i−iii-1-111-1-111i−i−iii−i−iii−i−ii
χ261111-1-1-1-1-1-1111-1-11-1-1-1-11111-111-1-111-1-11-1-1111111-1-1-1-1-1-1-1-111111-11-1−i−iiiii−i−i-1-111-1-111−iii−i−iii−i−iii−i
χ271111-1-1-1-1-1-1111-1-11-1-1-1-11111-111-1-1-1-1111-1-111-1-1-1-111111111-1-1-1-11-1-11ii−i−i−i−iii-1-11111-1-1i−i−ii−iii−i−iii−i
χ281111-1-1-1-1-1-1111-1-11-1-1-1-11111-111-1-1-1-1111-1-111-1-1-1-111111111-1-1-1-11-1-11−i−iiiii−i−i-1-11111-1-1−iii−ii−i−iii−i−ii
χ291111-1-1-1-1-1-1111-1-11-1-1-1-11111-1-1-11111-1-11-1-111-1-1-1-111111111-1-1-1-1-111-1ii−i−i−i−iii11-1-1-1-111−iii−ii−i−ii−iii−i
χ301111-1-1-1-1-1-1111-1-11-1-1-1-11111-1-1-11111-1-11-1-111-1-1-1-111111111-1-1-1-1-111-1−i−iiiii−i−i11-1-1-1-111i−i−ii−iii−ii−i−ii
χ311111-1-1-1-1-1-1111-1-11-1-1-1-11111-1-1-111-1-1111-1-1111111-1-1-1-1-1-1-1-11111-11-11ii−i−i−i−iii11-1-111-1-1−iii−i−iii−ii−i−ii
χ321111-1-1-1-1-1-1111-1-11-1-1-1-11111-1-1-111-1-1111-1-1111111-1-1-1-1-1-1-1-11111-11-11−i−iiiii−i−i11-1-111-1-1i−i−iii−i−ii−iii−i
χ332222222222-2-22-2-2222222222-200000000-2-2-2-2-2000000000000000000002-22-22-22-200000000000000000000
χ342222222222-2-22-2-2222222222-200000000-2-2-2-2-200000000000000000000-22-22-22-2200000000000000000000
χ352222222222-2-22-2-22-2-2-2-2-2-2-2-2-200000000-22222000000000000000000002-22-2-22-2200000000000000000000
χ362222222222-2-22-2-22-2-2-2-2-2-2-2-2-200000000-2222200000000000000000000-22-222-22-200000000000000000000
χ3722222222-2-222-222-200000000-222222222-2000022-2-222-2-200000000-2-2-2-20000000000000000000000000000
χ3822222222-2-222-222-200000000-22222-2-2-2-2-20000-2-222-2-22200000000-2-2220000000000000000000000000000
χ3922222222-2-222-222-200000000-2-2-2-2-22222-20000-2-222-2-2220000000022-2-20000000000000000000000000000
χ4022222222-2-222-222-200000000-2-2-2-2-2-2-2-2-2-2000022-2-222-2-20000000022220000000000000000000000000000
χ412222-2-2-2-22222-2-2-2-200000000222-2-222-2-2-2000022-2-2-2-22200000000-22-220000000000000000000000000000
χ422222-2-2-2-22222-2-2-2-200000000222-2-2-2-222-20000-2-22222-2-200000000-222-20000000000000000000000000000
χ432222-2-2-2-22222-2-2-2-2000000002-2-22222-2-2-20000-2-22222-2-2000000002-2-220000000000000000000000000000
χ442222-2-2-2-22222-2-2-2-2000000002-2-222-2-222-2000022-2-2-2-222000000002-22-20000000000000000000000000000
χ452222-2-2-2-2-2-2-2-222222222-2-2-2-2200000000-2-2-222000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ462222-2-2-2-2-2-2-2-222222222-2-2-2-2200000000-2-2-22200000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ472222-2-2-2-2-2-2-2-22222-2-2-2-22222200000000-222-2-2000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ482222-2-2-2-2-2-2-2-22222-2-2-2-22222200000000-222-2-200000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ4922-2-222-2-2002-202-20i2i2−i2−i2i2i2−i2−i202i−2i2i−2i2i−2i2i−2i0i2−i2i2−i22-2002-200i2i2−i2−i2i2i2−i2−i20000000000002−22−22−22−2000000000000
χ5022-2-222-2-2002-202-20i2i2−i2−i2i2i2−i2−i202i−2i2i−2i−2i2i−2i2i0i2−i2i2−i2-2200-2200−i2−i2i2i2−i2−i2i2i20000000000002−22−2−22−22000000000000
χ5122-2-222-2-2002-202-20i2i2−i2−i2i2i2−i2−i20−2i2i−2i2i2i−2i2i−2i0i2−i2i2−i2-2200-2200−i2−i2i2i2−i2−i2i2i2000000000000−22−222−22−2000000000000
χ5222-2-222-2-2002-202-20i2i2−i2−i2i2i2−i2−i20−2i2i−2i2i−2i2i−2i2i0i2−i2i2−i22-2002-200i2i2−i2−i2i2i2−i2−i2000000000000−22−22−22−22000000000000
χ5322-2-222-2-2002-202-20−i2−i2i2i2−i2−i2i2i202i−2i2i−2i2i−2i2i−2i0−i2i2−i2i22-2002-200−i2−i2i2i2−i2−i2i2i2000000000000−22−22−22−22000000000000
χ5422-2-222-2-2002-202-20−i2−i2i2i2−i2−i2i2i202i−2i2i−2i−2i2i−2i2i0−i2i2−i2i2-2200-2200i2i2−i2−i2i2i2−i2−i2000000000000−22−222−22−2000000000000
χ5522-2-222-2-2002-202-20−i2−i2i2i2−i2−i2i2i20−2i2i−2i2i2i−2i2i−2i0−i2i2−i2i2-2200-2200i2i2−i2−i2i2i2−i2−i20000000000002−22−2−22−22000000000000
χ5622-2-222-2-2002-202-20−i2−i2i2i2−i2−i2i2i20−2i2i−2i2i−2i2i−2i2i0−i2i2−i2i22-2002-200−i2−i2i2i2−i2−i2i2i20000000000002−22−22−22−2000000000000
χ5722-2-2-2-222002-20-220i2i2−i2−i2−i2−i2i2i202i−2i−2i2i2i−2i−2i2i0i2−i2−i2i22-200-2200i2i2−i2−i2−i2−i2i2i20000000000002−2−222−2−22000000000000
χ5822-2-2-2-222002-20-220i2i2−i2−i2−i2−i2i2i202i−2i−2i2i−2i2i2i−2i0i2−i2−i2i2-22002-200−i2−i2i2i2i2i2−i2−i20000000000002−2−22−222−2000000000000
χ5922-2-2-2-222002-20-220i2i2−i2−i2−i2−i2i2i20−2i2i2i−2i2i−2i−2i2i0i2−i2−i2i2-22002-200−i2−i2i2i2i2i2−i2−i2000000000000−222−22−2−22000000000000
χ6022-2-2-2-222002-20-220i2i2−i2−i2−i2−i2i2i20−2i2i2i−2i−2i2i2i−2i0i2−i2−i2i22-200-2200i2i2−i2−i2−i2−i2i2i2000000000000−222−2−222−2000000000000
χ6122-2-2-2-222002-20-220−i2−i2i2i2i2i2−i2−i202i−2i−2i2i2i−2i−2i2i0−i2i2i2−i22-200-2200−i2−i2i2i2i2i2−i2−i2000000000000−222−2−222−2000000000000
χ6222-2-2-2-222002-20-220−i2−i2i2i2i2i2−i2−i202i−2i−2i2i−2i2i2i−2i0−i2i2i2−i2-22002-200i2i2−i2−i2−i2−i2i2i2000000000000−222−22−2−22000000000000
χ6322-2-2-2-222002-20-220−i2−i2i2i2i2i2−i2−i20−2i2i2i−2i2i−2i−2i2i0−i2i2i2−i2-22002-200i2i2−i2−i2−i2−i2i2i20000000000002−2−22−222−2000000000000
χ6422-2-2-2-222002-20-220−i2−i2i2i2i2i2−i2−i20−2i2i2i−2i−2i2i2i−2i0−i2i2i2−i22-200-2200−i2−i2i2i2i2i2−i2−i20000000000002−2−222−2−22000000000000
χ6544444444-4-4-4-4-4-4-4-40000000040000000040000000000000000000000000000000000000000000000000000
χ664444-4-4-4-444-4-4-444-400000000-40000000040000000000000000000000000000000000000000000000000000
χ6744-4-444-4-400-440-4402i22i2−2i2−2i22i22i2−2i2−2i20000000000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ6844-4-444-4-400-440-440−2i2−2i22i22i2−2i2−2i22i22i200000000002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ6944-4-4-4-44400-4404-402i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ7044-4-4-4-44400-4404-40−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ714-44-44-44-4000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000002i2−2i2002i2−2i22-22-22-22-200000000000000000000000000000000
χ724-44-44-44-4000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000−2i22i200−2i22i2-22-22-22-2200000000000000000000000000000000
χ734-44-44-44-400000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000002i2−2i2002i2−2i2-22-22-22-2200000000000000000000000000000000
χ744-44-44-44-400000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000−2i22i200−2i22i22-22-22-22-200000000000000000000000000000000
χ754-44-4-44-44000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000002i2−2i200−2i22i22-22-2-22-2200000000000000000000000000000000
χ764-44-4-44-44000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000−2i22i2002i2−2i2-22-222-22-200000000000000000000000000000000
χ774-44-4-44-4400000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000002i2−2i200−2i22i2-22-222-22-200000000000000000000000000000000
χ784-44-4-44-4400000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000−2i22i2002i2−2i22-22-2-22-2200000000000000000000000000000000
χ794-4-444-4-444-400400-40000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000
χ804-4-444-4-444-400400-4000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000
χ814-4-444-4-44-4400-40044-4-444-4-4400000000000000000000000000000000000000000000000000000000000000
χ824-4-444-4-44-4400-4004-444-4-444-400000000000000000000000000000000000000000000000000000000000000
χ834-4-44-444-44-400-40044-4-44-444-400000000000000000000000000000000000000000000000000000000000000
χ844-4-44-444-44-400-4004-444-44-4-4400000000000000000000000000000000000000000000000000000000000000
χ854-4-44-444-4-4400400-40000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000
χ864-4-44-444-4-4400400-4000000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000

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