Finite Group Databasebeta

← Group #313682

Character table — Group #313682

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888224444444488888888444444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-1-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-11-1-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-11-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-11111-11-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111111-111-1-111-1-1-11
χ17222222222-22-22-22-200000000-22222-200002222-2-2-2-200000000-2-2002200-2-200000000000000000000
χ18222222222-22-22-22-200000000-22222-20000-2-2-2-2222200000000-2-200-2-2002200000000000000000000
χ19222222222-22-22-22-200000000-2-2-2-2-2-200002222-2-2-2-2000000002200-2-2002200000000000000000000
χ20222222222-22-22-22-200000000-2-2-2-2-2-20000-2-2-2-222220000000022002200-2-200000000000000000000
χ2122222222-22-22-22-2222222222-20000-2-2-2-2-20000000000000000002200220000000000-2-20000000000
χ2222222222-22-22-22-2222222222-20000-2-2-2-2-2000000000000000000-2-200-2-20000000000220000000000
χ2322222222-22-22-22-22-2-2-2-2-2-2-2-2-20000-222220000000000000000002200-2-200000000002-20000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2-2-2-20000-22222000000000000000000-2-200220000000000-220000000000
χ2522-22-22-2-2020-20-2022222-2-2-2-20000000000i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2002i−2i002i−2i00000000000000002−22−200
χ2622-22-22-2-2020-20-2022222-2-2-2-20000000000i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i200−2i2i00−2i2i0000000000000000−22−2200
χ2722-22-22-2-2020-20-2022222-2-2-2-20000000000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2002i−2i002i−2i0000000000000000−22−2200
χ2822-22-22-2-2020-20-2022222-2-2-2-20000000000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i200−2i2i00−2i2i00000000000000002−22−200
χ2922-22-22-2-2020-20-202-2-2-2-222220000000000i2i2−i2−i2i2i2−i2−i2−i2−i2−i2−i2i2i2i2i2002i−2i00−2i2i00000000000000002−2−2200
χ3022-22-22-2-2020-20-202-2-2-2-222220000000000i2i2−i2−i2i2i2−i2−i2−i2−i2−i2−i2i2i2i2i200−2i2i002i−2i0000000000000000−222−200
χ3122-22-22-2-2020-20-202-2-2-2-222220000000000−i2−i2i2i2−i2−i2i2i2i2i2i2i2−i2−i2−i2−i2002i−2i00−2i2i0000000000000000−222−200
χ3222-22-22-2-2020-20-202-2-2-2-222220000000000−i2−i2i2i2−i2−i2i2i2i2i2i2i2−i2−i2−i2−i200−2i2i002i−2i00000000000000002−2−2200
χ3322-2-22-22-220-20-2020i2i2−i2−i2i2i2−i2−i202i2i−2i−2i0i2i2−i2−i200002-22-2i2i2−i2−i2i2i2−i2−i2000000002i−2i22−2−222−2−2000000000000
χ3422-2-22-22-220-20-2020i2i2−i2−i2i2i2−i2−i202i2i−2i−2i0i2i2−i2−i20000-22-22−i2−i2i2i2−i2−i2i2i200000000−2i2i−2−22222−2−2000000000000
χ3522-2-22-22-220-20-2020i2i2−i2−i2i2i2−i2−i20−2i−2i2i2i0i2i2−i2−i200002-22-2i2i2−i2−i2i2i2−i2−i200000000−2i2i−2−222−2−222000000000000
χ3622-2-22-22-220-20-2020i2i2−i2−i2i2i2−i2−i20−2i−2i2i2i0i2i2−i2−i20000-22-22−i2−i2i2i2−i2−i2i2i2000000002i−2i22−2−2−2−222000000000000
χ3722-2-22-22-220-20-2020−i2−i2i2i2−i2−i2i2i202i2i−2i−2i0−i2−i2i2i200002-22-2−i2−i2i2i2−i2−i2i2i2000000002i−2i−2−222−2−222000000000000
χ3822-2-22-22-220-20-2020−i2−i2i2i2−i2−i2i2i202i2i−2i−2i0−i2−i2i2i20000-22-22i2i2−i2−i2i2i2−i2−i200000000−2i2i22−2−2−2−222000000000000
χ3922-2-22-22-220-20-2020−i2−i2i2i2−i2−i2i2i20−2i−2i2i2i0−i2−i2i2i200002-22-2−i2−i2i2i2−i2−i2i2i200000000−2i2i22−2−222−2−2000000000000
χ4022-2-22-22-220-20-2020−i2−i2i2i2−i2−i2i2i20−2i−2i2i2i0−i2−i2i2i20000-22-22i2i2−i2−i2i2i2−i2−i2000000002i−2i−2−22222−2−2000000000000
χ412-22-2-222-222-2-222-2-22i−2i2i−2i2i−2i2i−2i-22-22-222i−2i2i−2i00000000000000002-20000000000002i−2i2i−2i000000000000
χ422-22-2-222-222-2-222-2-22i−2i2i−2i2i−2i2i−2i-2-22-2222i−2i2i−2i0000000000000000-22000000000000−2i2i−2i2i000000000000
χ432-22-2-222-222-2-222-2-2−2i2i−2i2i−2i2i−2i2i-22-22-22−2i2i−2i2i00000000000000002-2000000000000−2i2i−2i2i000000000000
χ442-22-2-222-222-2-222-2-2−2i2i−2i2i−2i2i−2i2i-2-22-222−2i2i−2i2i0000000000000000-220000000000002i−2i2i−2i000000000000
χ452-22-2-222-22-2-222-2-220000000022-22-2-20000000000002i−2i2i−2i2i−2i2i−2i-22000000002i−2i2i−2i0000000000000000
χ462-22-2-222-22-2-222-2-220000000022-22-2-2000000000000−2i2i−2i2i−2i2i−2i2i-2200000000−2i2i−2i2i0000000000000000
χ472-22-2-222-22-2-222-2-22000000002-22-22-20000000000002i−2i2i−2i2i−2i2i−2i2-200000000−2i2i−2i2i0000000000000000
χ482-22-2-222-22-2-222-2-22000000002-22-22-2000000000000−2i2i−2i2i−2i2i−2i2i2-2000000002i−2i2i−2i0000000000000000
χ492-22-2-222-2-222-2-222-22i−2i2i−2i2i−2i2i−2i20000-2−2i2i−2i2i0000000000000000000000000000000000002-22i−2i000000
χ502-22-2-222-2-222-2-222-22i−2i2i−2i2i−2i2i−2i20000-2−2i2i−2i2i000000000000000000000000000000000000-22−2i2i000000
χ512-22-2-222-2-222-2-222-2−2i2i−2i2i−2i2i−2i2i20000-22i−2i2i−2i0000000000000000000000000000000000002-2−2i2i000000
χ522-22-2-222-2-222-2-222-2−2i2i−2i2i−2i2i−2i2i20000-22i−2i2i−2i000000000000000000000000000000000000-222i−2i000000
χ532-2-22-2-2222020-20-202−2−222−2−2202i−2i−2i2i02−2−222-22-200002−2−222−2−2200002i−2i0000−i2i2i2−i2−i2i2i2−i2000000000000
χ542-2-22-2-2222020-20-202−2−222−2−2202i−2i−2i2i02−2−22-22-220000−222−2−222−20000−2i2i0000i2−i2−i2i2−i2i2i2−i2000000000000
χ552-2-22-2-2222020-20-202−2−222−2−220−2i2i2i−2i02−2−222-22-200002−2−222−2−220000−2i2i0000i2−i2−i2i2i2−i2−i2i2000000000000
χ562-2-22-2-2222020-20-202−2−222−2−220−2i2i2i−2i02−2−22-22-220000−222−2−222−200002i−2i0000−i2i2i2−i2i2−i2−i2i2000000000000
χ572-2-22-2-2222020-20-20−222−2−222−202i−2i−2i2i0−222−22-22-20000−222−2−222−200002i−2i0000i2−i2−i2i2i2−i2−i2i2000000000000
χ582-2-22-2-2222020-20-20−222−2−222−202i−2i−2i2i0−222−2-22-2200002−2−222−2−220000−2i2i0000−i2i2i2−i2i2−i2−i2i2000000000000
χ592-2-22-2-2222020-20-20−222−2−222−20−2i2i2i−2i0−222−22-22-20000−222−2−222−20000−2i2i0000−i2i2i2−i2−i2i2i2−i2000000000000
χ602-2-22-2-2222020-20-20−222−2−222−20−2i2i2i−2i0−222−2-22-2200002−2−222−2−2200002i−2i0000i2−i2−i2i2−i2i2i2−i2000000000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ62444-4-4-4-44000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000002i2−2i2−2i22i2-2-22222-2-2000000000000000000000000000000
χ63444-4-4-4-44000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000−2i22i22i2−2i222-2-2-2-222000000000000000000000000000000
χ64444-4-4-4-4400000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000002i2−2i2−2i22i222-2-2-2-222000000000000000000000000000000
χ65444-4-4-4-4400000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000−2i22i22i2−2i2-2-22222-2-2000000000000000000000000000000
χ6644-44-44-4-40-404040-40000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ6744-44-44-4-40-404040-4000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ6844-4-44-44-4-404040-402i22i2−2i2−2i22i22i2−2i2−2i2000000−2i2−2i22i22i20000000000000000000000000000000000000000000000
χ6944-4-44-44-4-404040-40−2i2−2i22i22i2−2i2−2i22i22i20000002i22i2−2i2−2i20000000000000000000000000000000000000000000000
χ704-4444-4-4-40000000022−22−2222−222222−2200000000002i2−2i2−2i22i200002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ714-4444-4-4-40000000022−22−2222−222222−220000000000−2i22i22i2−2i20000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ724-4444-4-4-400000000−222222−2222−22−222200000000002i2−2i2−2i22i20000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ734-4444-4-4-400000000−222222−2222−22−22220000000000−2i22i22i2−2i200002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ744-44-4-444-4-4-444-4-44400000000-40000400000000000000000000000000000000000000000000000000
χ754-4-44-4-444-40-40404022−22−222222−22−2222000000−222222−220000000000000000000000000000000000000000000000
χ764-4-44-4-444-40-404040−222222−22−222222−2200000022−22−22220000000000000000000000000000000000000000000000
χ774-4-4-444-4404040-40-44i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ784-4-4-444-4404040-40-4−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000
χ794-4-4-444-440-40-404040000000000000000000000000022−2222−22−2222−2222000000000000000000000000000000
χ804-4-4-444-440-40-4040400000000000000000000000000−2222−222222−2222−22000000000000000000000000000000

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