Finite Group Databasebeta

← Group #229321

Character table — Group #229321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444444444444444444488888888888822444444448888888888888888882244444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ31111111111111111111111111-1-1-1-1111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111
χ5111111111111111111111-1-1-1-111111111111111111-1-1-1-11111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111
χ8111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-111111111-1-111-1-111-1-1
χ911111111111111111-1-1-1-111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111
χ1111111111111111111-1-1-1-11111-1-1-1-111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ1211111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-1111111-1-111-1-1-1-1
χ1511111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ1611111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ1711-11-11-1-1-111-1-1-1111ii−i−i11-1-1ii−i−i-1iiii−i−i−i−i11-1-11-1i−ii−ii−ii−i1-111-1-111-1-111-1-1ii−i−i1-11-1i−ii−ii−i
χ1811-11-11-1-1-111-1-1-1111ii−i−i11-1-1ii−i−i-1−i−i−i−iiiii11-1-11-1−iii−ii−i−ii1-111-1-1-1-111-1-111−i−iii-11-11i−ii−i−ii
χ1911-11-11-1-1-111-1-1-1111ii−i−i11-1-1−i−iii-1iiii−i−i−i−i-1-1111-1i−i−iii−ii−i-11-1-11111-1-1-1-111−i−iii-111-1i−i−ii−ii
χ2011-11-11-1-1-111-1-1-1111ii−i−i11-1-1−i−iii-1−i−i−i−iiiii-1-1111-1−ii−iii−i−ii-11-1-111-1-11111-1-1ii−i−i1-1-11i−i−iii−i
χ2111-11-11-1-1-111-1-1-1111ii−i−i-1-111ii−i−i-1iiii−i−i−i−i11-1-1-11−iii−ii−i−ii1-1-1-11111-1-111-1-1ii−i−i-11-11−ii−ii−ii
χ2211-11-11-1-1-111-1-1-1111ii−i−i-1-111ii−i−i-1−i−i−i−iiiii11-1-1-11i−ii−ii−ii−i1-1-1-111-1-111-1-111−i−iii1-11-1−ii−iii−i
χ2311-11-11-1-1-111-1-1-1111ii−i−i-1-111−i−iii-1iiii−i−i−i−i-1-111-11−ii−iii−i−ii-1111-1-111-1-1-1-111−i−iii1-1-11−iii−ii−i
χ2411-11-11-1-1-111-1-1-1111ii−i−i-1-111−i−iii-1−i−i−i−iiiii-1-111-11i−i−iii−ii−i-1111-1-1-1-11111-1-1ii−i−i-111-1−iii−i−ii
χ2511-11-11-1-1-111-1-1-1111−i−iii11-1-1ii−i−i-1iiii−i−i−i−i-1-1111-1i−ii−i−iii−i-11-1-111-1-11111-1-1−i−iii1-1-11−iii−i−ii
χ2611-11-11-1-1-111-1-1-1111−i−iii11-1-1ii−i−i-1−i−i−i−iiiii-1-1111-1−iii−i−ii−ii-11-1-11111-1-1-1-111ii−i−i-111-1−iii−ii−i
χ2711-11-11-1-1-111-1-1-1111−i−iii11-1-1−i−iii-1iiii−i−i−i−i11-1-11-1i−i−ii−iii−i1-111-1-1-1-111-1-111ii−i−i-11-11−ii−iii−i
χ2811-11-11-1-1-111-1-1-1111−i−iii11-1-1−i−iii-1−i−i−i−iiiii11-1-11-1−ii−ii−ii−ii1-111-1-111-1-111-1-1−i−iii1-11-1−ii−ii−ii
χ2911-11-11-1-1-111-1-1-1111−i−iii-1-111ii−i−i-1iiii−i−i−i−i-1-111-11−iii−i−ii−ii-1111-1-1-1-11111-1-1−i−iii-111-1i−i−iii−i
χ3011-11-11-1-1-111-1-1-1111−i−iii-1-111ii−i−i-1−i−i−i−iiiii-1-111-11i−ii−i−iii−i-1111-1-111-1-1-1-111ii−i−i1-1-11i−i−ii−ii
χ3111-11-11-1-1-111-1-1-1111−i−iii-1-111−i−iii-1iiii−i−i−i−i11-1-1-11−ii−ii−ii−ii1-1-1-111-1-111-1-111ii−i−i1-11-1i−ii−i−ii
χ3211-11-11-1-1-111-1-1-1111−i−iii-1-111−i−iii-1−i−i−i−iiiii11-1-1-11i−i−ii−iii−i1-1-1-11111-1-111-1-1−i−iii-11-11i−ii−ii−i
χ33222222222-22-2-222-2-2222200002222-20000000022220000-2-2-2-200-2-200000000000000000000000000
χ34222222222-22-2-222-2-222220000-2-2-2-2-200000000-2-2-2-2000022-2-2002200000000000000000000000000
χ35222222222-22-2-222-2-2-2-2-2-200002222-200000000-2-2-2-20000-2-222002200000000000000000000000000
χ36222222222-22-2-222-2-2-2-2-2-20000-2-2-2-2-20000000022220000222200-2-200000000000000000000000000
χ3722222222-22-222-2-22-2000022220000-222-2-222-2-20000-2-2220000-2-20000000000000000000000000000
χ3822222222-22-222-2-22-2000022220000-2-2-222-2-2220000-2-2-2-20000220000000000000000000000000000
χ3922222222-22-222-2-22-20000-2-2-2-20000-222-2-222-2-2000022-2-20000220000000000000000000000000000
χ4022222222-22-222-2-22-20000-2-2-2-20000-2-2-222-2-222000022220000-2-20000000000000000000000000000
χ4122-22-22-2-222-2-2-22-22-2000022-2-2000022i2i−2i−2i−2i−2i2i2i0000-222i−2i0000−2i2i0000000000000000000000000000
χ4222-22-22-2-222-2-2-22-22-2000022-2-200002−2i−2i2i2i2i2i−2i−2i0000-22−2i2i00002i−2i0000000000000000000000000000
χ4322-22-22-2-222-2-2-22-22-20000-2-222000022i2i−2i−2i−2i−2i2i2i00002-2−2i2i00002i−2i0000000000000000000000000000
χ4422-22-22-2-222-2-2-22-22-20000-2-22200002−2i−2i2i2i2i2i−2i−2i00002-22i−2i0000−2i2i0000000000000000000000000000
χ4522-22-22-2-2-2-2222-22-2-22i2i−2i−2i00002i2i−2i−2i20000000022-2-20000−2i2i−2i2i00-2200000000000000000000000000
χ4622-22-22-2-2-2-2222-22-2-22i2i−2i−2i0000−2i−2i2i2i200000000-2-22200002i−2i−2i2i002-200000000000000000000000000
χ4722-22-22-2-2-2-2222-22-2-2−2i−2i2i2i00002i2i−2i−2i200000000-2-2220000−2i2i2i−2i002-200000000000000000000000000
χ4822-22-22-2-2-2-2222-22-2-2−2i−2i2i2i0000−2i−2i2i2i20000000022-2-200002i−2i2i−2i00-2200000000000000000000000000
χ492-222-2-22-2-202002-2002-22-200002i−2i2i−2i0i2−i2i2−i2i2−i2i2−i22i−2i2i−2i0000000000000000i2−i2i2−i22−22−22−22−20000000000
χ502-222-2-22-2-202002-2002-22-200002i−2i2i−2i0−i2i2−i2i2−i2i2−i2i22i−2i2i−2i0000000000000000−i2i2−i2i2−22−22−22−220000000000
χ512-222-2-22-2-202002-2002-22-20000−2i2i−2i2i0i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i0000000000000000i2−i2i2−i2−22−22−22−220000000000
χ522-222-2-22-2-202002-2002-22-20000−2i2i−2i2i0−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i0000000000000000−i2i2−i2i22−22−22−22−20000000000
χ532-222-2-22-2-202002-200-22-2200002i−2i2i−2i0i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i0000000000000000−i2i2−i2i22−22−2−22−220000000000
χ542-222-2-22-2-202002-200-22-2200002i−2i2i−2i0−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i0000000000000000i2−i2i2−i2−22−222−22−20000000000
χ552-222-2-22-2-202002-200-22-220000−2i2i−2i2i0i2−i2i2−i2i2−i2i2−i22i−2i2i−2i0000000000000000−i2i2−i2i2−22−222−22−20000000000
χ562-222-2-22-2-202002-200-22-220000−2i2i−2i2i0−i2i2−i2i2−i2i2−i2i22i−2i2i−2i0000000000000000i2−i2i2−i22−22−2−22−220000000000
χ572-2-222-2-2220200-2-2002i−2i−2i2i00002-2-2202−22−2−22−22−2i2i2i−2i0000000000000000−i2i2i2−i22−2−22i2−i2−i2i20000000000
χ582-2-222-2-2220200-2-2002i−2i−2i2i00002-2-220−22−222−22−2−2i2i2i−2i0000000000000000i2−i2−i2i2−222−2−i2i2i2−i20000000000
χ592-2-222-2-2220200-2-2002i−2i−2i2i0000-222-202−22−2−22−222i−2i−2i2i0000000000000000−i2i2i2−i2−222−2−i2i2i2−i20000000000
χ602-2-222-2-2220200-2-2002i−2i−2i2i0000-222-20−22−222−22−22i−2i−2i2i0000000000000000i2−i2−i2i22−2−22i2−i2−i2i20000000000
χ612-2-222-2-2220200-2-200−2i2i2i−2i00002-2-2202−22−2−22−222i−2i−2i2i0000000000000000i2−i2−i2i22−2−22−i2i2i2−i20000000000
χ622-2-222-2-2220200-2-200−2i2i2i−2i00002-2-220−22−222−22−22i−2i−2i2i0000000000000000−i2i2i2−i2−222−2i2−i2−i2i20000000000
χ632-2-222-2-2220200-2-200−2i2i2i−2i0000-222-202−22−2−22−22−2i2i2i−2i0000000000000000i2−i2−i2i2−222−2i2−i2−i2i20000000000
χ642-2-222-2-2220200-2-200−2i2i2i−2i0000-222-20−22−222−22−2−2i2i2i−2i0000000000000000−i2i2i2−i22−2−22−i2i2i2−i20000000000
χ6544444444-4-4-4-4-4-4-4-44000000000000400000000000000000000000000000000000000000000000000
χ6644-44-44-4-44-4-4444-4-44000000000000-400000000000000000000000000000000000000000000000000
χ674-444-4-44-440-400-440000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ684-444-4-44-440-400-44000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ694-44-4-44-440404-400-4000004i−4i4i−4i0000000000000000000000000000000000000000000000000000000
χ704-44-4-44-440404-400-400000−4i4i−4i4i0000000000000000000000000000000000000000000000000000000
χ714-44-4-44-440-40-440040000000000000000000000000000000000000022−2222−220000000000000000000000
χ724-44-4-44-440-40-4400400000000000000000000000000000000000000−2222−22220000000000000000000000
χ734-4-444-4-44-40-4004400000000000000022−22−2222−222222−22000000000000000000000000000000000000000000
χ744-4-444-4-44-40-40044000000000000000−222222−2222−22−2222000000000000000000000000000000000000000000
χ754-4-4-4444-4040-4400-4000004i−4i−4i4i0000000000000000000000000000000000000000000000000000000
χ764-4-4-4444-4040-4400-400000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000
χ774-4-4-4444-40-404-40040000000000000000000000000000000000000022−22−22220000000000000000000000
χ784-4-4-4444-40-404-400400000000000000000000000000000000000000−222222−220000000000000000000000
χ79888-88-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000
χ8088-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000

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