Finite Group Databasebeta

← Group #10822197

Character table — Group #10822197

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12442222222344444446661212121266666612121212121222224444444466666666121212121212121212121212121212122244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ611111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ911-1-11-1-1-1-111111-1-1-111111-1-1-1-111-1-1-1-11111-1-1111-1-1-11-111-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-11-11-111-1-111-1-111-1-1
χ1011-1-11-1-1-1-111111-1-1-111111-1-1-1-111-1-1-1-11111-1-1111-1-1-11-111-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-11-11-1-111-1-111-1-111
χ1111-1-11-1-1-1-111111-1-1-111111-1-1-1-111-1-1-1-11111-1-111-11-1-1-11-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1111-11-1-1-11111-1-1-1-111
χ1211-1-11-1-1-1-111111-1-1-111111-1-1-1-111-1-1-1-11111-1-111-11-1-1-11-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-111-11-1111-1-1-1-11111-1-1
χ1311-1-11-1-1-1-111111-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-11-1111-1-1-111-1-1-1-111-1-1-1-1-1-11111111111-1-11-11-1-1-111-1-11111-1-1
χ1411-1-11-1-1-1-111111-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-11-1111-1-1-111-1-1-1-111-1-1-1-1-1-11111111111-1-1-11-1111-1-111-1-1-1-111
χ1511-1-11-1-1-1-111111-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-1-1111-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111-11-111-1-1-1-111-1-111
χ1611-1-11-1-1-1-111111-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-1-1111-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-11-11-1-11111-1-111-1-1
χ1722222222222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-2-2-2-1-1-1-1111111111111-1-1-1-111110000000000000000
χ1922222222222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-2-2-21111-1-1-1-1111111111111-1-1-1-10000000000000000
χ2022222222222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ212222222-2-2-2-22222-2-2-2-2-2-2222-2-22-222-2-222-2-22-200000000000000000000000000000000000000002i−2i2i−2i00000000
χ222222222-2-2-2-22222-2-2-2-2-2-2222-2-22-222-2-222-2-22-20000000000000000000000000000000000000000−2i2i−2i2i00000000
χ2322222-2-222-2-22-2-22-2-222-2-2222-2-22-2-2-222-2-2222-20000000000000000000000000000000000002-2-22000000000000
χ2422222-2-222-2-22-2-22-2-222-2-2222-2-22-2-2-222-2-2222-2000000000000000000000000000000000000-222-2000000000000
χ2522222-2-2-2-2222-2-2222-2-2222222222-2-2-2-2-2-2-2-222000000002-22-20000000022-2-222-2-2000000000000000000000000
χ2622222-2-2-2-2222-2-2222-2-2222222222-2-2-2-2-2-2-2-22200000000-22-2200000000-2-222-2-222000000000000000000000000
χ2722222-2-2-2-222-1-2-2222-2-2-1-1-1-1-1-1-1-1-111111111-1-1000000002-22-2−i3−i3i3i3−i3i3−i3i3-1-111-1-111−i3−i3i3i3−i3i3−i3i30000000000000000
χ2822222-2-2-2-222-1-2-2222-2-2-1-1-1-1-1-1-1-1-111111111-1-1000000002-22-2i3i3−i3−i3i3−i3i3−i3-1-111-1-111i3i3−i3−i3i3−i3i3−i30000000000000000
χ2922222-2-2-2-222-1-2-2222-2-2-1-1-1-1-1-1-1-1-111111111-1-100000000-22-22−i3−i3i3i3i3−i3i3−i311-1-111-1-1−i3−i3i3i3i3−i3i3−i30000000000000000
χ3022222-2-2-2-222-1-2-2222-2-2-1-1-1-1-1-1-1-1-111111111-1-100000000-22-22i3i3−i3−i3−i3i3−i3i311-1-111-1-1i3i3−i3−i3−i3i3−i3i30000000000000000
χ312222-22-22-22-222-2-22-22-22222222-2-22-22-22-22-2-2-2002-200-220000000022-2-2000000000000-2-2220000000000000000
χ322222-22-22-22-222-2-22-22-22222222-2-22-22-22-22-2-2-200-22002-200000000-2-22200000000000022-2-20000000000000000
χ332222-22-22-22-2-12-2-22-22-2-1-1-1-1-1-1-111-11-11-11-1111002-200-220000−i3i3−i3i3-1-111−i3i3−i3i3−i3i3−i3i3−i3i3−i3i311-1-10000000000000000
χ342222-22-22-22-2-12-2-22-22-2-1-1-1-1-1-1-111-11-11-11-1111002-200-220000i3−i3i3−i3-1-111i3−i3i3−i3i3−i3i3−i3i3−i3i3−i311-1-10000000000000000
χ352222-22-22-22-2-12-2-22-22-2-1-1-1-1-1-1-111-11-11-11-111100-22002-20000−i3i3−i3i311-1-1i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3-1-1110000000000000000
χ362222-22-22-22-2-12-2-22-22-2-1-1-1-1-1-1-111-11-11-11-111100-22002-20000i3−i3i3−i311-1-1−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3-1-1110000000000000000
χ372222-22-2-22-2222-2-2-22-22-2-2222-2-2-222-2-222-2-22-22000000000000000000000000000000000000000000002-22-20000
χ382222-22-2-22-2222-2-2-22-22-2-2222-2-2-222-2-222-2-22-2200000000000000000000000000000000000000000000-22-220000
χ392222-2-222-2-222-22-2-222-2-2-2222-2-2-22-222-2-222-2-220000000000000000000000000000000000000000000000002-22-2
χ402222-2-222-2-222-22-2-222-2-2-2222-2-2-22-222-2-222-2-22000000000000000000000000000000000000000000000000-22-22
χ412222-2-22-222-22-22-22-2-222222222-2-2-22-22-22-22-2-22-2002-20000002-2-220000000000002-2-2200000000000000000000
χ422222-2-22-222-22-22-22-2-222222222-2-2-22-22-22-22-2-2-2200-22000000-222-2000000000000-222-200000000000000000000
χ432222-2-22-222-2-1-22-22-2-22-1-1-1-1-1-1-1111-11-11-11-1112-2002-2000000-111-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3-111-1i3−i3−i3i30000000000000000
χ442222-2-22-222-2-1-22-22-2-22-1-1-1-1-1-1-1111-11-11-11-1112-2002-2000000-111-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3-111-1−i3i3i3−i30000000000000000
χ452222-2-22-222-2-1-22-22-2-22-1-1-1-1-1-1-1111-11-11-11-111-2200-220000001-1-11−i3i3i3−i3i3−i3−i3i3i3−i3−i3i31-1-11i3−i3−i3i30000000000000000
χ462222-2-22-222-2-1-22-22-2-22-1-1-1-1-1-1-1111-11-11-11-111-2200-220000001-1-11i3−i3−i3i3−i3i3i3−i3−i3i3i3−i31-1-11−i3i3i3−i30000000000000000
χ4722-2-222222222-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2000000002-2-220000000022-2-2-2-222000000000000000000000000
χ4822-2-222222222-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-200000000-222-200000000-2-22222-2-2000000000000000000000000
χ4922-2-22222222-1-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111000000002-2-22−i3−i3i3i3−i3i3i3−i3-1-11111-1-1i3i3−i3−i3−i3i3i3−i30000000000000000
χ5022-2-22222222-1-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111000000002-2-22i3i3−i3−i3i3−i3−i3i3-1-11111-1-1−i3−i3i3i3i3−i3−i3i30000000000000000
χ5122-2-22222222-1-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-111111100000000-222-2−i3−i3i3i3i3−i3−i3i311-1-1-1-111i3i3−i3−i3i3−i3−i3i30000000000000000
χ5222-2-22222222-1-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-111111100000000-222-2i3i3−i3−i3−i3i3i3−i311-1-1-1-111−i3−i3i3i3−i3i3i3−i30000000000000000
χ5322-2-2222-2-2-2-22-2-2-22222-2-22-2-2222-222-2-2-2-222-2200000000000000000000000000000000000022-2-2000000000000
χ5422-2-2222-2-2-2-22-2-2-22222-2-22-2-2222-222-2-2-2-222-22000000000000000000000000000000000000-2-222000000000000
χ5522-2-22-2-222-2-2222-222-2-2-2-22-2-2222-2-2-22222-2-2-2200000000000000000000000000000000000000002i−2i−2i2i00000000
χ5622-2-22-2-222-2-2222-222-2-2-2-22-2-2222-2-2-22222-2-2-220000000000000000000000000000000000000000−2i2i2i−2i00000000
χ5722-2-22-2-2-2-222-122-2-2-222-1-1-11111-1-11111-1-1-1-111222-2-2-22-222-2-2-1-1-1-1-1-111-1-1-1-111111111-1-1110000000000000000
χ5822-2-22-2-2-2-222-122-2-2-222-1-1-11111-1-11111-1-1-1-11122-22-2-2-22-2-222-1-1-1-111-1-11111-1-1-1-1111111-1-10000000000000000
χ5922-2-22-2-2-2-222-122-2-2-222-1-1-11111-1-11111-1-1-1-111-2-22-2222-2-2-2221111-1-1111111-1-1-1-1-1-1-1-1-1-1110000000000000000
χ6022-2-22-2-2-2-222-122-2-2-222-1-1-11111-1-11111-1-1-1-111-2-2-2222-2222-2-2111111-1-1-1-1-1-11111-1-1-1-111-1-10000000000000000
χ6122-2-2-22-22-22-22-222-22-22222-2-2-2-2-2-22-22-2-22-22222-200-220000002-2-22000000000000-222-200000000000000000000
χ6222-2-2-22-22-22-22-222-22-22222-2-2-2-2-2-22-22-2-22-2222-22002-2000000-222-20000000000002-2-2200000000000000000000
χ6322-2-2-22-22-22-2-1-222-22-22-1-1-1111111-11-111-11-1-1-12-200-22000000-111-1−i3i3−i3i3−i3i3i3−i3i3−i3−i3i31-1-11i3−i3i3−i30000000000000000
χ6422-2-2-22-22-22-2-1-222-22-22-1-1-1111111-11-111-11-1-1-12-200-22000000-111-1i3−i3i3−i3i3−i3−i3i3−i3i3i3−i31-1-11−i3i3−i3i30000000000000000
χ6522-2-2-22-22-22-2-1-222-22-22-1-1-1111111-11-111-11-1-1-1-22002-20000001-1-11−i3i3−i3i3i3−i3−i3i3−i3i3i3−i3-111-1i3−i3i3−i30000000000000000
χ6622-2-2-22-22-22-2-1-222-22-22-1-1-1111111-11-111-11-1-1-1-22002-20000001-1-11i3−i3i3−i3−i3i3i3−i3i3−i3−i3i3-111-1−i3i3−i3i30000000000000000
χ6722-2-2-22-2-22-222-2222-22-2-2-22-2-222-222-2-22-222-22-20000000000000000000000000000000000000000000000002-2-22
χ6822-2-2-22-2-22-222-2222-22-2-2-22-2-222-222-2-22-222-22-2000000000000000000000000000000000000000000000000-222-2
χ6922-2-2-2-222-2-2222-222-2-22-2-22-2-222-22-222-22-2-222-2000000000000000000000000000000000000000000002-2-220000
χ7022-2-2-2-222-2-2222-222-2-22-2-22-2-222-22-222-22-2-222-200000000000000000000000000000000000000000000-222-20000
χ7122-2-2-2-22-222-222-22-222-2222-2-2-2-2-2-2-22-222-22-222002200-2-2000000002222000000000000-2-2-2-20000000000000000
χ7222-2-2-2-22-222-222-22-222-2222-2-2-2-2-2-2-22-222-22-22200-2-2002200000000-2-2-2-200000000000022220000000000000000
χ7322-2-2-2-22-222-2-12-22-222-2-1-1-11111111-11-1-11-11-1-1002200-2-20000−i3i3−i3i3-1-1-1-1−i3i3−i3i3i3−i3i3−i3i3−i3i3−i311110000000000000000
χ7422-2-2-2-22-222-2-12-22-222-2-1-1-11111111-11-1-11-11-1-1002200-2-20000i3−i3i3−i3-1-1-1-1i3−i3i3−i3−i3i3−i3i3−i3i3−i3i311110000000000000000
χ7522-2-2-2-22-222-2-12-22-222-2-1-1-11111111-11-1-11-11-1-100-2-200220000−i3i3−i3i31111i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3-1-1-1-10000000000000000
χ7622-2-2-2-22-222-2-12-22-222-2-1-1-11111111-11-1-11-11-1-100-2-200220000i3−i3i3−i31111−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3-1-1-1-10000000000000000
χ774444444-4-4-4-4-2444-4-4-4-422-2-2-222-22-2-222-2-222-220000000000000000000000000000000000000000000000000000
χ7844444-4-444-4-4-2-4-44-4-44422-2-2-222-2222-2-222-2-2-220000000000000000000000000000000000000000000000000000
χ794444-44-4-44-44-24-4-4-44-4422-2-2-2222-2-222-2-222-22-20000000000000000000000000000000000000000000000000000
χ804444-4-444-4-44-2-44-4-444-422-2-2-2222-22-2-222-2-222-20000000000000000000000000000000000000000000000000000
χ8144-4-4444-4-4-4-4-2-4-4-4444422-222-2-2-22-2-22222-2-22-20000000000000000000000000000000000000000000000000000
χ8244-4-44-4-444-4-4-244-444-4-422-222-2-2-2222-2-2-2-2222-20000000000000000000000000000000000000000000000000000
χ8344-4-4-44-4-44-44-2-4444-44-422-222-2-22-2-222-22-2-22-220000000000000000000000000000000000000000000000000000
χ8444-4-4-4-444-4-44-24-444-4-4422-222-2-22-22-2-22-222-2-220000000000000000000000000000000000000000000000000000
χ858-88i−8i00000008000000000-88i−8i000000000000000000000000000000000000000000000000000000000000000000
χ868-88i−8i0000000-40000000−4i34i34−4i4i43−430000000000000000000000000000000000000000000000000000000000000000
χ878-88i−8i0000000-400000004i3−4i34−4i4i−43430000000000000000000000000000000000000000000000000000000000000000
χ888-8−8i8i00000008000000000-8−8i8i000000000000000000000000000000000000000000000000000000000000000000
χ898-8−8i8i0000000-40000000−4i34i344i−4i−43430000000000000000000000000000000000000000000000000000000000000000
χ908-8−8i8i0000000-400000004i3−4i344i−4i43−430000000000000000000000000000000000000000000000000000000000000000

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