Finite Group Databasebeta

← Group #186664

Character table — Group #186664

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222222244444444444444444444444444448888888888888888222222444444444444448888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-11-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-11-1-1-1-111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111111111-1-1-1-1
χ911111111-1-1-1-1111-1-1-1-111-1-1-1-1111-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1111-1-1-1-111-1-1-1-1111-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ1111111111-1-1-1-1111-1-1-1-111-1-1-1-1111-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ1211111111-1-1-1-1111-1-1-1-111-1-1-1-1111-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1111-1-1-1-111-1-1-1-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111
χ1411111111-1-1-1-1111-1-1-1-111-1-1-1-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-11111-1-11111-1-1
χ1511111111-1-1-1-1111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1
χ1611111111-1-1-1-1111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-11111-1-11111-1-1-1-111-1-1-1-111
χ171-1-11-1-11111-1-111-111-1-11111-1-1-1-1-11-111-1-1111-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11-11-11-11-11-111-1-11-1ii−i−iii−i−ii−ii−ii−ii−i
χ181-1-11-1-11111-1-111-111-1-11111-1-1-1-1-11-111-1-1111-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-11-111-1-111-1-1-111-11ii−i−iii−i−i−ii−ii−ii−ii
χ191-1-11-1-11111-1-111-111-1-11111-1-1-1-1-11-111-1-1111-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11-11-11-11-11-111-1-11-1−i−iii−i−iii−ii−ii−ii−ii
χ201-1-11-1-11111-1-111-111-1-11111-1-1-1-1-11-111-1-1111-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-11-111-1-111-1-1-111-11−i−iii−i−iiii−ii−ii−ii−i
χ211-1-11-1-11111-1-111-111-1-11111-1-1-1-1-11-1-1-1111-1-111-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-11-11-11-11-1111-1-1-11−i−iii−i−iiii−ii−i−ii−ii
χ221-1-11-1-11111-1-111-111-1-11111-1-1-1-1-11-1-1-1111-1-111-1iiii−i−i−i−iiiii−i−i−i−i-1-1111-11-1-111-1-11-1-1111-1−i−iii−i−iii−ii−iii−ii−i
χ231-1-11-1-11111-1-111-111-1-11111-1-1-1-1-11-1-1-1111-1-111-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-11-11-11-11-1111-1-1-11ii−i−iii−i−i−ii−iii−ii−i
χ241-1-11-1-11111-1-111-111-1-11111-1-1-1-1-11-1-1-1111-1-111-1−i−i−i−iiiii−i−i−i−iiiii-1-1111-11-1-111-1-11-1-1111-1ii−i−iii−i−ii−ii−i−ii−ii
χ251-1-11-1-111-1-11111-1-1-11111-1-111-1-1-1-1111-1-11-1-111-1iiii−i−i−i−i−i−i−i−iiiii11-1-11-1-11-111-11-1-1-111-11ii−i−i−i−iiii−i−iii−i−ii
χ261-1-11-1-111-1-11111-1-1-11111-1-111-1-1-1-1111-1-11-1-111-1iiii−i−i−i−i−i−i−i−iiiii-1-111-111-1-11-111-111-1-11-1ii−i−i−i−iii−iii−i−iii−i
χ271-1-11-1-111-1-11111-1-1-11111-1-111-1-1-1-1111-1-11-1-111-1−i−i−i−iiiiiiiii−i−i−i−i11-1-11-1-11-111-11-1-1-111-11−i−iiiii−i−i−iii−i−iii−i
χ281-1-11-1-111-1-11111-1-1-11111-1-111-1-1-1-1111-1-11-1-111-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-111-1-11-111-111-1-11-1−i−iiiii−i−ii−i−iii−i−ii
χ291-1-11-1-111-1-11111-1-1-11111-1-111-1-1-1-11-1-111111-1-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-111-11-1-11-11-1-1111-1−i−iiiii−i−ii−i−ii−iii−i
χ301-1-11-1-111-1-11111-1-1-11111-1-111-1-1-1-11-1-111111-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1111-1-111-11-1-1111-1-1-11−i−iiiii−i−i−iii−ii−i−ii
χ311-1-11-1-111-1-11111-1-1-11111-1-111-1-1-1-11-1-111111-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-111-11-1-11-11-1-1111-1ii−i−i−i−iii−iii−ii−i−ii
χ321-1-11-1-111-1-11111-1-1-11111-1-111-1-1-1-11-1-111111-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1-111-11-1-1111-1-1-11ii−i−i−i−iiii−i−ii−iii−i
χ332222222222222222222-2-2-2-2-2-2-2-22-2-20000-20000-20000000000000000000022-2-200-2-2000000220000000000000000
χ342222222222222222222-2-2-2-2-2-2-2-22-2-20000-20000-200000000000000000000-2-2220022000000-2-20000000000000000
χ35222222222222-2-2-2-2-2-2-222-2-2-2-222-2222222-2-2-2-2-2-20000000000000000000000002200-2-20000000000000000000000
χ36222222222222-2-2-2-2-2-2-222-2-2-2-222-222-2-2-2-2-22222-2000000000000000000000000-2-200220000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2000020000200000000000000002-22-200000000002-22-2000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-200002000020000000000000000-22-220000000000-22-22000000000000000000
χ3922222222-2-2-2-2222-2-2-2-2-2-22222-2-22220000-20000-200000000000000000000222200-2-2000000-2-20000000000000000
χ4022222222-2-2-2-2222-2-2-2-2-2-22222-2-22220000-20000-200000000000000000000-2-2-2-20022000000220000000000000000
χ4122222222-2-2-2-2-2-2-2222222222222-2-2-22222-22222-2000000000000000000000000-2-200-2-20000000000000000000000
χ4222222222-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002200220000000000000000000000
χ4322222222-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-222000020000200000000000000002-22-20000000000-22-22000000000000000000
χ4422222222-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-22200002000020000000000000000-22-2200000000002-22-2000000000000000000
χ4522-2-22-22-200000002i−2i2i−2i2-22i−2i2i−2i2-20002-22-202i−2i2i−2i0i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000000000000000i2−i2i2−i22−22−200000000
χ4622-2-22-22-200000002i−2i2i−2i2-22i−2i2i−2i2-20002-22-202i−2i2i−2i0−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000000000000000−i2i2−i2i2−22−2200000000
χ4722-2-22-22-200000002i−2i2i−2i2-22i−2i2i−2i2-2000-22-220−2i2i−2i2i0i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000000000000000−i2i2−i2i2−22−2200000000
χ4822-2-22-22-200000002i−2i2i−2i2-22i−2i2i−2i2-2000-22-220−2i2i−2i2i0−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000000000000000i2−i2i2−i22−22−200000000
χ4922-2-22-22-20000000−2i2i−2i2i2-2−2i2i−2i2i2-20002-22-20−2i2i−2i2i0i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000000000000000i2−i2i2−i2−22−2200000000
χ5022-2-22-22-20000000−2i2i−2i2i2-2−2i2i−2i2i2-20002-22-20−2i2i−2i2i0−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000000000000000−i2i2−i2i22−22−200000000
χ5122-2-22-22-20000000−2i2i−2i2i2-2−2i2i−2i2i2-2000-22-2202i−2i2i−2i0i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000000000000000−i2i2−i2i22−22−200000000
χ5222-2-22-22-20000000−2i2i−2i2i2-2−2i2i−2i2i2-2000-22-2202i−2i2i−2i0−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000000000000000i2−i2i2−i2−22−2200000000
χ532-22-2-222-200000002i−2i−2i2i2-22i−2i−2i2i-220002-2-2202i−2i−2i2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−22−i2i2i2−i200000000
χ542-22-2-222-200000002i−2i−2i2i2-22i−2i−2i2i-220002-2-2202i−2i−2i2i0−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000000000−222−2i2−i2−i2i200000000
χ552-22-2-222-200000002i−2i−2i2i2-22i−2i−2i2i-22000-222-20−2i2i2i−2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000000000−222−2i2−i2−i2i200000000
χ562-22-2-222-200000002i−2i−2i2i2-22i−2i−2i2i-22000-222-20−2i2i2i−2i0−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−22−i2i2i2−i200000000
χ572-22-2-222-20000000−2i2i2i−2i2-2−2i2i2i−2i-220002-2-220−2i2i2i−2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−22i2−i2−i2i200000000
χ582-22-2-222-20000000−2i2i2i−2i2-2−2i2i2i−2i-220002-2-220−2i2i2i−2i0−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000000000−222−2−i2i2i2−i200000000
χ592-22-2-222-20000000−2i2i2i−2i2-2−2i2i2i−2i-22000-222-202i−2i−2i2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000000000−222−2−i2i2i2−i200000000
χ602-22-2-222-20000000−2i2i2i−2i2-2−2i2i2i−2i-22000-222-202i−2i−2i2i0−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−22i2−i2−i2i200000000
χ612-2-22-2-22222-2-222-222-2-2-2-2-2-22222-2-220000-200002000000000000000000002-2-2200-220000002-20000000000000000
χ622-2-22-2-22222-2-222-222-2-2-2-2-2-22222-2-220000-20000200000000000000000000-222-2002-2000000-220000000000000000
χ632-2-22-2-22222-2-2-2-22-2-22222-2-222-2-222-222-2-2-2-2-22220000000000000000000000002-200-220000000000000000000000
χ642-2-22-2-22222-2-2-2-22-2-22222-2-222-2-222-2-2-222-222-2-22000000000000000000000000-22002-20000000000000000000000
χ652-2-22-2-22222-2-2-2-22-2-222-2-222-2-2222-22000020000-200000000000000002-2-2200000000002-2-22000000000000000000
χ662-2-22-2-22222-2-2-2-22-2-222-2-222-2-2222-22000020000-20000000000000000-222-20000000000-222-2000000000000000000
χ672-2-22-2-222-2-22222-2-2-222-2-222-2-222-22-20000-200002000000000000000000002-22-200-22000000-220000000000000000
χ682-2-22-2-222-2-22222-2-2-222-2-222-2-222-22-20000-20000200000000000000000000-22-22002-20000002-20000000000000000
χ692-2-22-2-222-2-222-2-2222-2-22222-2-2-2-22-2222-2-2-222-2-22000000000000000000000000-2200-220000000000000000000000
χ702-2-22-2-222-2-222-2-2222-2-22222-2-2-2-22-22-2-222-2-2-22220000000000000000000000002-2002-20000000000000000000000
χ712-2-22-2-222-2-222-2-2222-2-2-2-2-2-2222222-2000020000-200000000000000002-2-220000000000-222-2000000000000000000
χ722-2-22-2-222-2-222-2-2222-2-2-2-2-2-2222222-2000020000-20000000000000000-222-200000000002-2-22000000000000000000
χ73444-4-4-4-444-44-400000000000000000000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ74444-4-4-4-444-44-40000000000000000000000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ75444-4-4-4-44-44-4400000000000000000000000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ76444-4-4-4-44-44-440000000000000000000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ7744-44-44-4-400004-44000000000000-400000000000022−22−222222−22−222200000000000000000000000000000000000000000000
χ7844-44-44-4-400004-44000000000000-4000000000000−222222−22−222222−2200000000000000000000000000000000000000000000
χ7944-44-44-4-40000-44-40000000000004000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ8044-44-44-4-40000-44-4000000000000400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ8144-4-44-44-400000004i−4i4i−4i-44−4i4i−4i4i-4400000000000000000000000000000000000000000000000000000000000000000
χ8244-4-44-44-40000000−4i4i−4i4i-444i−4i4i−4i-4400000000000000000000000000000000000000000000000000000000000000000
χ834-4444-4-4-400004-4-400000000000040000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ844-4444-4-4-400004-4-40000000000004000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ854-4444-4-4-40000-444000000000000-40000000000000000000022−22−2222−222222−22000000000000000000000000000000000000
χ864-4444-4-4-40000-444000000000000-400000000000000000000−222222−2222−22−2222000000000000000000000000000000000000
χ874-44-4-444-400000004i−4i−4i4i-44−4i4i4i−4i4-400000000000000000000000000000000000000000000000000000000000000000
χ884-44-4-444-40000000−4i4i4i−4i-444i−4i−4i4i4-400000000000000000000000000000000000000000000000000000000000000000
χ894-4-4-444-444-4-4400000000000000000000000000002-22-2-22-222-22-2-22-22000000000000000000000000000000000000
χ904-4-4-444-444-4-440000000000000000000000000000-22-222-22-2-22-222-22-2000000000000000000000000000000000000
χ914-4-4-444-44-444-400000000000000000000000000002-22-2-22-22-22-222-22-2000000000000000000000000000000000000
χ924-4-4-444-44-444-40000000000000000000000000000-22-222-22-22-22-2-22-22000000000000000000000000000000000000

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