Finite Group Databasebeta

← Group #290207

Character table — Group #290207

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444444444444488888888888888884444444448888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ9111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-11
χ10111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-11-1
χ11111111111111111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11-1
χ12111111111111111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1111111-1-11111-1-1-1-1111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1111111-1-111-1-1-1-1-1-111111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-11
χ17222222222-222-2-22-2-2-222-2-2-2-2000000002222-2-2-2-2200000000220000-2-200000000000000
χ18222222222-222-2-22-2-2-222-2-2-2-200000000-2-2-2-22222200000000-2-200002200000000000000
χ19222222222-222-2-22-2-2-2-2-222220000000022222222-200000000-2-20000-2-200000000000000
χ20222222222-222-2-22-2-2-2-2-2222200000000-2-2-2-2-2-2-2-2-2000000002200002200000000000000
χ2122222222-22-2-222-22-2-222-2-2220000000000000000-222-2-222-2-20000000000000000000000
χ2222222222-22-2-222-22-2-222-2-2220000000000000000-2-2-222-2-2220000000000000000000000
χ2322222222-22-2-222-22-2-2-2-222-2-20000000000000000222-2-2-2-2220000000000000000000000
χ2422222222-22-2-222-22-2-2-2-222-2-200000000000000002-2-22222-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2222222-2-22i2i2i2i−2i−2i−2i−2i00000000-200000000002i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-2222222-2-2−2i−2i−2i−2i2i2i2i2i00000000-20000000000−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-2-2-2222i2i2i2i−2i−2i−2i−2i0000000020000000000−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-2-2-222−2i−2i−2i−2i2i2i2i2i00000000200000000002i2i−2i−2i0000000000000000
χ29222-2-22-2-2222-22-2-2-22-200000022-2-222-2-200000000000000000000000002-2002-200000000
χ30222-2-22-2-2222-22-2-2-22-200000022-2-222-2-20000000000000000000000000-2200-2200000000
χ31222-2-22-2-2222-22-2-2-22-2000000-2-222-2-22200000000000000000000000002-200-2200000000
χ32222-2-22-2-2222-22-2-2-22-2000000-2-222-2-2220000000000000000000000000-22002-200000000
χ33222-2-22-2-2-2-2-22-22222-20000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000002i−2i00002-20000
χ34222-2-22-2-2-2-2-22-22222-20000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000−2i2i0000-220000
χ35222-2-22-2-2-2-2-22-22222-2000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000002i−2i0000-220000
χ36222-2-22-2-2-2-2-22-22222-2000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000−2i2i00002-20000
χ372-2-22-222-20200-2-202002i−2i002i−2ii2−i2i2−i2i2−i2i2−i2i2i2−i2−i222−2−20002-2002i−2i2−22−22−2i2−i200000000000000
χ382-2-22-222-20200-2-202002i−2i002i−2ii2−i2i2−i2i2−i2i2−i2−i2−i2i2i2−2−222000-2200−2i2i−222−22−2−i2i200000000000000
χ392-2-22-222-20200-2-202002i−2i002i−2i−i2i2−i2i2−i2i2−i2i2i2i2−i2−i222−2−2000-2200−2i2i2−2−22−22i2−i200000000000000
χ402-2-22-222-20200-2-202002i−2i002i−2i−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−2−2220002-2002i−2i−22−22−22−i2i200000000000000
χ412-2-22-222-20200-2-20200−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i2i2i2−i2−i2−2−2220002-200−2i2i−22−22−22i2−i200000000000000
χ422-2-22-222-20200-2-20200−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i2−i2−i2i2i222−2−2000-22002i−2i2−2−22−22−i2i200000000000000
χ432-2-22-222-20200-2-20200−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i2i2i2−i2−i2−2−222000-22002i−2i−222−22−2i2−i200000000000000
χ442-2-22-222-20200-2-20200−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i2−i2−i2i2i222−2−20002-200−2i2i2−22−22−2−i2i200000000000000
χ452-2-22-222-20-200220-2002i−2i00−2i2i2−22−2−22−22i2i2−i2−i2−2−22202i−2i002-2002−2−i2i2i2−i2−i2i200000000000000
χ462-2-22-222-20-200220-2002i−2i00−2i2i2−22−2−22−22−i2−i2i2i222−2−20−2i2i00-2200−22−i2i2i2−i2i2−i200000000000000
χ472-2-22-222-20-200220-2002i−2i00−2i2i−22−222−22−2i2i2−i2−i2−2−2220−2i2i00-22002−2i2−i2−i2i2−i2i200000000000000
χ482-2-22-222-20-200220-2002i−2i00−2i2i−22−222−22−2−i2−i2i2i222−2−202i−2i002-200−22i2−i2−i2i2i2−i200000000000000
χ492-2-22-222-20-200220-200−2i2i002i−2i2−22−2−22−22i2i2−i2−i222−2−202i−2i00-2200−22i2−i2−i2i2−i2i200000000000000
χ502-2-22-222-20-200220-200−2i2i002i−2i2−22−2−22−22−i2−i2i2i2−2−2220−2i2i002-2002−2i2−i2−i2i2i2−i200000000000000
χ512-2-22-222-20-200220-200−2i2i002i−2i−22−222−22−2i2i2−i2−i222−2−20−2i2i002-200−22−i2i2i2−i2−i2i200000000000000
χ522-2-22-222-20-200220-200−2i2i002i−2i−22−222−22−2−i2−i2i2i2−2−22202i−2i00-22002−2−i2i2i2−i2i2−i200000000000000
χ53444-4-44-4-44-44-4-44-44-4400000000000000000000000000000000000000000000000000000
χ54444-4-44-4-4-44-444-44-4-4400000000000000000000000000000000000000000000000000000
χ5544-444-4-4-440-4-40040000000000000000000004-44-40000000000000000000000000000000
χ5644-444-4-4-440-4-4004000000000000000000000-44-440000000000000000000000000000000
χ5744-444-4-4-4-404400-4000000000000000004-44-400000000000000000000000000000000000
χ5844-444-4-4-4-404400-400000000000000000-44-4400000000000000000000000000000000000
χ5944-4-4-4-44440-4400-40000000000000000000000000000000000000000000000002i2−2i2000000
χ6044-4-4-4-44440-4400-4000000000000000000000000000000000000000000000000−2i22i2000000
χ6144-4-4-4-444-404-4004000000000000000000000000000000000000000000000000000022−2200
χ6244-4-4-4-444-404-40040000000000000000000000000000000000000000000000000000−222200
χ634-444-4-4-440000000000004i−4i00000000002i2−2i2−2i22i222−22−22220000000000000000000000000000000
χ644-444-4-4-440000000000004i−4i0000000000−2i22i22i2−2i2−222222−220000000000000000000000000000000
χ654-444-4-4-44000000000000−4i4i00000000002i2−2i2−2i22i2−222222−220000000000000000000000000000000
χ664-444-4-4-44000000000000−4i4i0000000000−2i22i22i2−2i222−22−22220000000000000000000000000000000
χ674-4-4-444-440400-440-4000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000
χ684-4-4-444-440400-440-400000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000
χ694-4-4-444-440-4004-4040000000022−22−2222−222222−22000000000000000000000000000000000000000
χ704-4-4-444-440-4004-40400000000−222222−2222−22−2222000000000000000000000000000000000000000
χ718-88-88-88-8000000000000000000000000000000000000000000000000000000000000000

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