Finite Group Databasebeta

← Group #223159

Character table — Group #223159

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11111111222222222222222222224444444444444444444444444444448888888888888888888888888888888161616161616
order12222222222244444444444444442244444444444488888888888888884444444888888888888888888888888224444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11111-1-1iiii−i−i−i−iii−i−iii−i−iiiii−i−i−i−i1-11-11-1
χ61111111111111111-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii111-1-111iiii−i−i−i−i−i−iiiii−i−i−i−i−i−iiiii-11-11-11
χ71111111111111111-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i111-1-111−i−i−i−iiiiiii−i−i−i−iiiiiii−i−i−i−i-11-11-11
χ81111111111111111-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11111-1-1−i−i−i−iiiii−i−iii−i−iii−i−i−i−iiiii1-11-11-1
χ9111111111111-1-1-1-1111-1-1-1-111111-1-1-1-1111111-1-1-1-11111111111111111-11-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111
χ10111111111111-1-1-1-1111-1-1-1-111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1
χ11111111111111-1-1-1-1111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ12111111111111-1-1-1-1111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111111111111111-1-1-1-1-1-111-1-111-1-1-1-111
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-11-111-1-1−i−i−i−iiiii−i−iiiii−i−iii−i−i−i−iii-11-111-1
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11-1-1-111−i−i−i−iiiiiii−i−iii−i−i−i−iiiii−i−i1-11-1-11
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-11-1-1-111iiii−i−i−i−i−i−iii−i−iiiii−i−i−i−iii1-11-1-11
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-11-111-1-1iiii−i−i−i−iii−i−i−i−iii−i−iiiii−i−i-11-111-1
χ1711111111-1-1-1-11111111-1-1-1-11111111-1-111-1-1-1-111-1-11111111111111111-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ1811111111-1-1-1-11111111-1-1-1-11111111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-111
χ1911111111-1-1-1-11111111-1-1-1-11111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-11111-1-111
χ2011111111-1-1-1-11111111-1-1-1-11111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1111111111111-1-111-1-1-1-111-1-1
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111iiii−i−i−i−iiiii−i−i−i−i-1-1111-1-1ii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−i-111-1-11
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii1-1-111-1
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i1-1-111-1
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111−i−i−i−iiiii−i−i−i−iiiii-1-1111-1-1−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii-111-1-11
χ2511111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-11111111111111111111-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ2611111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-11111
χ2711111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ2811111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-111-1-1-1-1-1-111111111111111-1-1-1-1
χ2911111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-111111111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-111-1-1−i−iiiii−i−iii−i−i−i−iii−i−i−i−iiiii1-1-11-11
χ3011111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-1-1-111−i−iiiii−i−i−i−iii−i−iiiiiii−i−i−i−i-111-11-1
χ3111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1-111ii−i−i−i−iiiii−i−iii−i−i−i−i−i−iiiii-111-11-1
χ3211111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-111111111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-111-1-1ii−i−i−i−iii−i−iiiii−i−iiiii−i−i−i−i1-1-11-11
χ33222222222222222222-222222-2-2-2222-2-2-2-222-2-2-2-2220000000000000000-2-2-20000000000000000000000000000000000
χ342222222222222222-2-222222-2222-2-2-222-2-2-2-22222-2-20000000000000000-2-2-20000000000000000000000000000000000
χ35222222222222-2-2-2-222-2-2-2-2-22-2-2-22-2-222-2-222-2-222-2-200000000000000002-220000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-22-2-2-2-2-2222-222-2-2-2-2-2-222-2-22200000000000000002-220000000000000000000000000000000000
χ3722222222-2-2-2-2222222-2-2-2-2-22-2-2-222222-2-2-2-222-2-2-2-2000000000000000022-20000000000000000000000000000000000
χ3822222222-2-2-2-22222-2-22-2-2-2-2-2222-2-2-2-2-2-2-222-2-22222000000000000000022-20000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222-222222-2-2-22-2-2-2-2-2-2-2-22222220000000000000000-2220000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-222222-2222-22222-2-222-2-2-2-2-2-20000000000000000-2220000000000000000000000000000000000
χ4122-22-2-22-222-2-22i2i−2i−2i0022i2i−2i−2i0-2-220002i−2i00002-22i−2i0000000000i2i2−i2−i2i2i2−i2−i20000000000000002−22−20000i2−i22−2i2−i22−2000000
χ4222-22-2-22-222-2-22i2i−2i−2i0022i2i−2i−2i0-2-220002i−2i00002-22i−2i0000000000−i2−i2i2i2−i2−i2i2i2000000000000000−22−220000−i2i2−22−i2i2−22000000
χ4322-22-2-22-222-2-22i2i−2i−2i00-22i2i−2i−2i022-2000−2i2i0000-22−2i2i000000000022−2−2−2−222000000000000000−i2i2i2−i200002−2−i2i2−22i2−i2000000
χ4422-22-2-22-222-2-22i2i−2i−2i00-22i2i−2i−2i022-2000−2i2i0000-22−2i2i0000000000−2−22222−2−2000000000000000i2−i2−i2i20000−22i2−i22−2−i2i2000000
χ4522-22-2-22-222-2-2−2i−2i2i2i002−2i−2i2i2i0-2-22000−2i2i00002-2−2i2i0000000000i2i2−i2−i2i2i2−i2−i2000000000000000−22−220000i2−i2−22i2−i2−22000000
χ4622-22-2-22-222-2-2−2i−2i2i2i002−2i−2i2i2i0-2-22000−2i2i00002-2−2i2i0000000000−i2−i2i2i2−i2−i2i2i20000000000000002−22−20000−i2i22−2−i2i22−2000000
χ4722-22-2-22-222-2-2−2i−2i2i2i00-2−2i−2i2i2i022-20002i−2i0000-222i−2i000000000022−2−2−2−222000000000000000i2−i2−i2i200002−2i2−i2−22−i2i2000000
χ4822-22-2-22-222-2-2−2i−2i2i2i00-2−2i−2i2i2i022-20002i−2i0000-222i−2i0000000000−2−22222−2−2000000000000000−i2i2i2−i20000−22−i2i22−2i2−i2000000
χ4922-22-2-22-2-2-2222i2i−2i−2i002−2i−2i2i2i0-2-22000−2i2i0000-222i−2i0000000000i2i2−i2−i2i2i2−i2−i2000000000000000−22−220000−i2i22−2−i2i22−2000000
χ5022-22-2-22-2-2-2222i2i−2i−2i002−2i−2i2i2i0-2-22000−2i2i0000-222i−2i0000000000−i2−i2i2i2−i2−i2i2i20000000000000002−22−20000i2−i2−22i2−i2−22000000
χ5122-22-2-22-2-2-2222i2i−2i−2i00-2−2i−2i2i2i022-20002i−2i00002-2−2i2i000000000022−2−2−2−222000000000000000i2−i2−i2i20000−22−i2i22−2i2−i2000000
χ5222-22-2-22-2-2-2222i2i−2i−2i00-2−2i−2i2i2i022-20002i−2i00002-2−2i2i0000000000−2−22222−2−2000000000000000−i2i2i2−i200002−2i2−i2−22−i2i2000000
χ5322-22-2-22-2-2-222−2i−2i2i2i0022i2i−2i−2i0-2-220002i−2i0000-22−2i2i0000000000i2i2−i2−i2i2i2−i2−i20000000000000002−22−20000−i2i2−22−i2i2−22000000
χ5422-22-2-22-2-2-222−2i−2i2i2i0022i2i−2i−2i0-2-220002i−2i0000-22−2i2i0000000000−i2−i2i2i2−i2−i2i2i2000000000000000−22−220000i2−i22−2i2−i22−2000000
χ5522-22-2-22-2-2-222−2i−2i2i2i00-22i2i−2i−2i022-2000−2i2i00002-22i−2i000000000022−2−2−2−222000000000000000−i2i2i2−i20000−22i2−i22−2−i2i2000000
χ5622-22-2-22-2-2-222−2i−2i2i2i00-22i2i−2i−2i022-2000−2i2i00002-22i−2i0000000000−2−22222−2−2000000000000000i2−i2−i2i200002−2−i2i2−22i2−i2000000
χ572-2-2222-2-2000000002-220000-22-2-2200002-2000000002i2i−2i−2i2i2i−2i−2i2-22-22-22-20002i−2i2i−2i000000000000000000000000000000
χ582-2-2222-2-2000000002-220000-22-2-2200002-2000000002i2i−2i−2i2i2i−2i−2i-22-22-22-22000−2i2i−2i2i000000000000000000000000000000
χ592-2-2222-2-2000000002-220000-22-2-2200002-200000000−2i−2i2i2i−2i−2i2i2i2-22-22-22-2000−2i2i−2i2i000000000000000000000000000000
χ602-2-2222-2-2000000002-220000-22-2-2200002-200000000−2i−2i2i2i−2i−2i2i2i-22-22-22-220002i−2i2i−2i000000000000000000000000000000
χ612-2-2222-2-200000000-22-200002-222-200002-20000000022-2-2-2-2222i−2i2i−2i−2i2i−2i2i000−2i2i2i−2i000000000000000000000000000000
χ622-2-2222-2-200000000-22-200002-222-200002-20000000022-2-2-2-222−2i2i−2i2i2i−2i2i−2i0002i−2i−2i2i000000000000000000000000000000
χ632-2-2222-2-200000000-22-200002-222-200002-200000000-2-22222-2-22i−2i2i−2i−2i2i−2i2i0002i−2i−2i2i000000000000000000000000000000
χ642-2-2222-2-200000000-22-200002-222-200002-200000000-2-22222-2-2−2i2i−2i2i2i−2i2i−2i000−2i2i2i−2i000000000000000000000000000000
χ652-2-2-22-2222-22-22-22-22202-22-2-2000-22-200002-200002-2i2−i2i2−i2i2−i2i2−i2000000000000000i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i200000000000000
χ662-2-2-22-2222-22-22-22-22202-22-2-2000-22-200002-200002-2−i2i2−i2i2−i2i2−i2i2000000000000000−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i200000000000000
χ672-2-2-22-2222-22-22-22-2-2-202-22-220002-220000-220000-222−22−2−22−220000000000000002−22−2−22−2200002−2−2200000000000000
χ682-2-2-22-2222-22-22-22-2-2-202-22-220002-220000-220000-22−22−222−22−2000000000000000−22−222−22−20000−222−200000000000000
χ692-2-2-22-2222-22-2-22-22220-22-22-2000-2-2200002-20000-22i2−i2i2−i2i2−i2i2−i2000000000000000−i2i2−i2i2−i2i2−i2i20000i2−i2i2−i200000000000000
χ702-2-2-22-2222-22-2-22-22220-22-22-2000-2-2200002-20000-22−i2i2−i2i2−i2i2−i2i2000000000000000i2−i2i2−i2i2−i2i2−i20000−i2i2−i2i200000000000000
χ712-2-2-22-2222-22-2-22-22-2-20-22-22200022-20000-2200002-22−22−2−22−22000000000000000−22−222−22−200002−2−2200000000000000
χ722-2-2-22-2222-22-2-22-22-2-20-22-22200022-20000-2200002-2−22−222−22−20000000000000002−22−2−22−220000−222−200000000000000
χ732-2-2-22-222-22-222-22-2220-22-22-2000-22-20000-220000-22i2−i2i2−i2i2−i2i2−i2000000000000000i2−i2−i2i2i2−i2−i2i20000−i2i2−i2i200000000000000
χ742-2-2-22-222-22-222-22-2220-22-22-2000-22-20000-220000-22−i2i2−i2i2−i2i2−i2i2000000000000000−i2i2i2−i2−i2i2i2−i20000i2−i2i2−i200000000000000
χ752-2-2-22-222-22-222-22-2-2-20-22-2220002-2200002-200002-22−22−2−22−220000000000000002−2−22−222−20000−222−200000000000000
χ762-2-2-22-222-22-222-22-2-2-20-22-2220002-2200002-200002-2−22−222−22−2000000000000000−222−22−2−2200002−2−2200000000000000
χ772-2-2-22-222-22-22-22-222202-22-2-2000-2-220000-2200002-2i2−i2i2−i2i2−i2i2−i2000000000000000−i2i2i2−i2−i2i2i2−i20000−i2i2−i2i200000000000000
χ782-2-2-22-222-22-22-22-222202-22-2-2000-2-220000-2200002-2−i2i2−i2i2−i2i2−i2i2000000000000000i2−i2−i2i2i2−i2−i2i20000i2−i2i2−i200000000000000
χ792-2-2-22-222-22-22-22-22-2-202-22-2200022-200002-20000-222−22−2−22−22000000000000000−222−22−2−220000−222−200000000000000
χ802-2-2-22-222-22-22-22-22-2-202-22-2200022-200002-20000-22−22−222−22−20000000000000002−2−22−222−200002−2−2200000000000000
χ81444-44-4-4-4000000004-4000004000-40000000000000022−22−222222−22−2222000000000000000000000000000000000000000000000
χ82444-44-4-4-4000000004-4000004000-400000000000000−222222−22−222222−22000000000000000000000000000000000000000000000
χ83444-44-4-4-400000000-4400000-40004000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000000
χ84444-44-4-4-400000000-4400000-4000400000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000000
χ854-444-4-4-440000000000400000-44-4000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000
χ864-444-4-4-440000000000400000-44-400000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000
χ874-444-4-4-440000000000-4000004-440000000000000000000000022−22−2222−222222−220000000000000000000000000000000000000
χ884-444-4-4-440000000000-4000004-4400000000000000000000000−222222−2222−22−22220000000000000000000000000000000000000
χ894-44-4-444-44-4-444i−4i−4i4i0004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ904-44-4-444-44-4-44−4i4i4i−4i000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ914-44-4-444-4-444-44i−4i−4i4i000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ924-44-4-444-4-444-4−4i4i4i−4i0004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ934-4-4444-4-4000000004-4-40000-4-44440000-440000000000000000000000000000000000000000000000000000000000000
χ944-4-4444-4-400000000-444000044-4-4-40000-440000000000000000000000000000000000000000000000000000000000000
χ9588-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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