Finite Group Databasebeta

← Group #307413

Character table — Group #307413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888224444444488888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ61111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ71111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111111-1-11-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-111-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1111-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-11111111-1-1-111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1111-1-111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-1-111-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1111111-1-1-1-1-1111-1-1-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-11-1-1-11111-1-1-11
χ17222222222-222-2-22-200000000-22222-200002222-2-2-2-20000000000-2-22200-2-200000000000000000000
χ18222222222-222-2-22-200000000-22222-20000-2-2-2-222220000000000-2-2-2-2002200000000000000000000
χ19222222222-222-2-22-200000000-2-2-2-2-2-200002222-2-2-2-2000000000022-2-2002200000000000000000000
χ20222222222-222-2-22-200000000-2-2-2-2-2-20000-2-2-2-222220000000000222200-2-200000000000000000000
χ2122222222-22-2-222-2222222222-20000-2-2-2-2-20000000000000000220000220000000000-200-200000000
χ2222222222-22-2-222-2222222222-20000-2-2-2-2-20000000000000000-2-20000-2-20000000000200200000000
χ2322222222-22-2-222-22-2-2-2-2-2-2-2-2-20000-222220000000000000000220000-2-20000000000200-200000000
χ2422222222-22-2-222-22-2-2-2-2-2-2-2-2-20000-222220000000000000000-2-20000220000000000-200200000000
χ25222-22-2-2-2-202-200202222−2−2−2−202i2i−2i−2i022−2−2000022-2-22222−2−2−2−2000000002i−2ii2i2−i2−i2i2i2−i2−i2000000000000
χ26222-22-2-2-2-202-200202222−2−2−2−202i2i−2i−2i022−2−20000-2-222−2−2−2−2222200000000−2i2ii2i2−i2−i2−i2−i2i2i2000000000000
χ27222-22-2-2-2-202-200202222−2−2−2−20−2i−2i2i2i022−2−2000022-2-22222−2−2−2−200000000−2i2i−i2−i2i2i2−i2−i2i2i2000000000000
χ28222-22-2-2-2-202-200202222−2−2−2−20−2i−2i2i2i022−2−20000-2-222−2−2−2−22222000000002i−2i−i2−i2i2i2i2i2−i2−i2000000000000
χ29222-22-2-2-2-202-20020−2−2−2−2222202i2i−2i−2i0−2−222000022-2-2−2−2−2−22222000000002i−2i−i2−i2i2i2−i2−i2i2i2000000000000
χ30222-22-2-2-2-202-20020−2−2−2−2222202i2i−2i−2i0−2−2220000-2-2222222−2−2−2−200000000−2i2i−i2−i2i2i2i2i2−i2−i2000000000000
χ31222-22-2-2-2-202-20020−2−2−2−222220−2i−2i2i2i0−2−222000022-2-2−2−2−2−2222200000000−2i2ii2i2−i2−i2i2i2−i2−i2000000000000
χ32222-22-2-2-2-202-20020−2−2−2−222220−2i−2i2i2i0−2−2220000-2-2222222−2−2−2−2000000002i−2ii2i2−i2−i2−i2−i2i2i2000000000000
χ332-22-2-22-2202002-20-22i2i−2i−2i2i2i−2i−2i000000000022−2−22−22−2i2i2−i2−i2i2i2−i2−i22-200002i−2i00000000000000002−2i2−i200
χ342-22-2-22-2202002-20-22i2i−2i−2i2i2i−2i−2i000000000022−2−22−22−2i2i2−i2−i2i2i2−i2−i2-220000−2i2i0000000000000000−22−i2i200
χ352-22-2-22-2202002-20-22i2i−2i−2i2i2i−2i−2i0000000000−2−222−22−22−i2−i2i2i2−i2−i2i2i22-200002i−2i0000000000000000−22−i2i200
χ362-22-2-22-2202002-20-22i2i−2i−2i2i2i−2i−2i0000000000−2−222−22−22−i2−i2i2i2−i2−i2i2i2-220000−2i2i00000000000000002−2i2−i200
χ372-22-2-22-2202002-20-2−2i−2i2i2i−2i−2i2i2i000000000022−2−22−22−2−i2−i2i2i2−i2−i2i2i22-20000−2i2i00000000000000002−2−i2i200
χ382-22-2-22-2202002-20-2−2i−2i2i2i−2i−2i2i2i000000000022−2−22−22−2−i2−i2i2i2−i2−i2i2i2-2200002i−2i0000000000000000−22i2−i200
χ392-22-2-22-2202002-20-2−2i−2i2i2i−2i−2i2i2i0000000000−2−222−22−22i2i2−i2−i2i2i2−i2−i22-20000−2i2i0000000000000000−22i2−i200
χ402-22-2-22-2202002-20-2−2i−2i2i2i−2i−2i2i2i0000000000−2−222−22−22i2i2−i2−i2i2i2−i2−i2-2200002i−2i00000000000000002−2−i2i200
χ412-2-222-2-22202-200-202−22−22−22−202-22-202−22−22i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i200002i−2i00002−22−2i2−i2i2−i2000000000000
χ422-2-222-2-22202-200-202−22−22−22−202-22-202−22−2−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i20000−2i2i00002−22−2−i2i2−i2i2000000000000
χ432-2-222-2-22202-200-202−22−22−22−20-22-2202−22−22i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i20000−2i2i0000−22−22−i2i2−i2i2000000000000
χ442-2-222-2-22202-200-202−22−22−22−20-22-2202−22−2−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i200002i−2i0000−22−22i2−i2i2−i2000000000000
χ452-2-222-2-22202-200-20−22−22−22−2202-22-20−22−222i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i200002i−2i0000−22−22−i2i2−i2i2000000000000
χ462-2-222-2-22202-200-20−22−22−22−2202-22-20−22−22−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i20000−2i2i0000−22−22i2−i2i2−i2000000000000
χ472-2-222-2-22202-200-20−22−22−22−220-22-220−22−222i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i20000−2i2i00002−22−2i2−i2i2−i2000000000000
χ482-2-222-2-22202-200-20−22−22−22−220-22-220−22−22−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i200002i−2i00002−22−2−i2i2−i2i2000000000000
χ492-2-2-2222-22-2-2-2222-22-22-2-22-2220000-2-222-2000000000000000000000000000000000002i−2i02i−2i000000
χ502-2-2-2222-22-2-2-2222-22-22-2-22-2220000-2-222-200000000000000000000000000000000000−2i2i0−2i2i000000
χ512-2-2-2222-22-2-2-2222-2-22-222-22-220000-22-2-22000000000000000000000000000000000002i−2i0−2i2i000000
χ522-2-2-2222-22-2-2-2222-2-22-222-22-220000-22-2-2200000000000000000000000000000000000−2i2i02i−2i000000
χ532-2-2-2222-2-2222-2-2-220000000022i−2i−2i2i-20000000000002i−2i2i−2i−2i2i−2i2i002i−2i0000000000-222-2000000000000
χ542-2-2-2222-2-2222-2-2-220000000022i−2i−2i2i-2000000000000−2i2i−2i2i2i−2i2i−2i002i−2i00000000002-2-22000000000000
χ552-2-2-2222-2-2222-2-2-22000000002−2i2i2i−2i-20000000000002i−2i2i−2i−2i2i−2i2i00−2i2i00000000002-2-22000000000000
χ562-2-2-2222-2-2222-2-2-22000000002−2i2i2i−2i-2000000000000−2i2i−2i2i2i−2i2i−2i00−2i2i0000000000-222-2000000000000
χ572-2-2-2222-2-2-22222-2-22-22-2-22-22-22i−2i−2i2i22-2-22000000000000000000−2i2i0000002i−2i−2i2i0000000000000000
χ582-2-2-2222-2-2-22222-2-22-22-2-22-22-2−2i2i2i−2i22-2-220000000000000000002i−2i000000−2i2i2i−2i0000000000000000
χ592-2-2-2222-2-2-22222-2-2-22-222-22-2-22i−2i−2i2i2-222-2000000000000000000−2i2i000000−2i2i2i−2i0000000000000000
χ602-2-2-2222-2-2-22222-2-2-22-222-22-2-2−2i2i2i−2i2-222-20000000000000000002i−2i0000002i−2i−2i2i0000000000000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ62444-44-4-4-440-4400-4022222222−22−22−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ63444-44-4-4-440-4400-40−22−22−22−22222222220000002222−22−220000000000000000000000000000000000000000000000
χ6444-44-44-4-40400-440-40000000000000000000000000022−22−2222−222222−22000000000000000000000000000000
χ6544-44-44-4-40400-440-400000000000000000000000000−222222−2222−22−2222000000000000000000000000000000
χ6644-44-44-4-40-4004-4044i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ6744-44-44-4-40-4004-404−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ6844-4-4-4-444000000002i2−2i2−2i22i22i2−2i2−2i22i200000000002i2−2i2−2i22i20000-222-2-222-2000000000000000000000000000000
χ6944-4-4-4-444000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000−2i22i22i2−2i200002-2-222-2-22000000000000000000000000000000
χ7044-4-4-4-44400000000−2i22i22i2−2i2−2i22i22i2−2i200000000002i2−2i2−2i22i200002-2-222-2-22000000000000000000000000000000
χ7144-4-4-4-44400000000−2i22i22i2−2i2−2i22i22i2−2i20000000000−2i22i22i2−2i20000-222-2-222-2000000000000000000000000000000
χ724-444-4-44-4000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000022−22−22222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ734-444-4-44-4000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000−222222−22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ744-444-4-44-400000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000022−22−2222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ754-444-4-44-400000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000−222222−222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ764-44-4-44-440-400-44040000000000000000002222−22−22−2222−222200000000000000000000000000000000000000
χ774-44-4-44-440-400-4404000000000000000000−22−22222222−2222−2200000000000000000000000000000000000000
χ784-4-444-4-44-40-44004022−2222−2222−2222−22000000−2222−22220000000000000000000000000000000000000000000000
χ794-4-444-4-44-40-440040−2222−2222−2222−222200000022−2222−220000000000000000000000000000000000000000000000
χ804-4-4-4444-444-4-4-4-44400000000-40000400000000000000000000000000000000000000000000000000

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