Finite Group Databasebeta

← Group #306387

Character table — Group #306387

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-111-1-1111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ511111111111111111111-1-1-1-111111111111111-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1111-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-111-1-1-1-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-11111111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111-1-111-111-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-11111-111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-11111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1-1111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111111-1-11-1-1-1-1-1-11
χ17222222222-22-22-22-200002222-2-200002222000022-2-2-2-20000000000000000000-20000000
χ18222222222-22-22-22-200002222-2-20000-2-2-2-20000-2-2-2-222000000000000000000020000000
χ19222222222-22-22-22-20000-2-2-2-2-2-2000022220000-2-222-2-2000000000000000000020000000
χ20222222222-22-22-22-20000-2-2-2-2-2-20000-2-2-2-200002222220000000000000000000-20000000
χ2122222222-22-22-22-2222220000-2-222220000-2-2220000000000-2-200000000-2000000000000
χ2222222222-22-22-22-2222220000-2-2-2-2-2-20000-2-2-2-2000000000022000000002000000000000
χ2322222222-22-22-22-22-2-2-2-20000-2-22222000022-2-20000000000-2-2000000002000000000000
χ2422222222-22-22-22-22-2-2-2-20000-2-2-2-2-2-20000222200000000002200000000-2000000000000
χ25222-2-2-22-20-20-202022i2i−2i−2i0000002i2i−2i−2i22−2−2002-200002−2000000i2i2−i2−i2i2i2−i2−i2000000002−2000
χ26222-2-2-22-20-20-202022i2i−2i−2i0000002i2i−2i−2i−2−222002-20000−22000000−i2−i2i2i2−i2−i2i2i200000000−22000
χ27222-2-2-22-20-20-202022i2i−2i−2i000000−2i−2i2i2i22−2−200-2200002−2000000i2i2−i2−i2−i2−i2i2i200000000−22000
χ28222-2-2-22-20-20-202022i2i−2i−2i000000−2i−2i2i2i−2−22200-220000−22000000−i2−i2i2i2i2i2−i2−i2000000002−2000
χ29222-2-2-22-20-20-20202−2i−2i2i2i0000002i2i−2i−2i22−2−200-2200002−2000000−i2−i2i2i2i2i2−i2−i200000000−22000
χ30222-2-2-22-20-20-20202−2i−2i2i2i0000002i2i−2i−2i−2−22200-220000−22000000i2i2−i2−i2−i2−i2i2i2000000002−2000
χ31222-2-2-22-20-20-20202−2i−2i2i2i000000−2i−2i2i2i22−2−2002-200002−2000000−i2−i2i2i2−i2−i2i2i2000000002−2000
χ32222-2-2-22-20-20-20202−2i−2i2i2i000000−2i−2i2i2i−2−222002-20000−22000000i2i2−i2−i2i2i2−i2−i200000000−22000
χ332-222-22-2-22-2-222-2-222-22-20000-22000000002-2000000002i2i−2i−2i00000000000002i−2i00000000
χ342-222-22-2-22-2-222-2-222-22-20000-22000000002-200000000−2i−2i2i2i0000000000000−2i2i00000000
χ352-222-22-2-22-2-222-2-22-22-220000-2200000000-22000000002i2i−2i−2i0000000000000−2i2i00000000
χ362-222-22-2-22-2-222-2-22-22-220000-2200000000-2200000000−2i−2i2i2i00000000000002i−2i00000000
χ372-222-22-2-2-222-2-222-200002i2i−2i−2i-22000000000000002i−2i000000002-22-200000000002i−2i00000
χ382-222-22-2-2-222-2-222-200002i2i−2i−2i-22000000000000002i−2i00000000-22-220000000000−2i2i00000
χ392-222-22-2-2-222-2-222-20000−2i−2i2i2i-2200000000000000−2i2i000000002-22-20000000000−2i2i00000
χ402-222-22-2-2-222-2-222-20000−2i−2i2i2i-2200000000000000−2i2i00000000-22-2200000000002i−2i00000
χ412-222-22-2-2-2-222-2-2222-22-22i2i−2i−2i2-200000000-220000−2i2i000000000000000002i−2i0000000000
χ422-222-22-2-2-2-222-2-2222-22-2−2i−2i2i2i2-200000000-2200002i−2i00000000000000000−2i2i0000000000
χ432-222-22-2-2-2-222-2-222-22-222i2i−2i−2i2-2000000002-20000−2i2i00000000000000000−2i2i0000000000
χ442-222-22-2-2-2-222-2-222-22-22−2i−2i2i2i2-2000000002-200002i−2i000000000000000002i−2i0000000000
χ452-2-222-22-220-20-202000002-22-200i2−i2i2−i22-22-200002-20000i2−i2i2−i2i2−i20000i2−i2i2−i20000000000i2−i20
χ462-2-222-22-220-20-202000002-22-200i2−i2i2−i2-22-220000-220000i2−i2i2−i2i2−i20000−i2i2−i2i20000000000−i2i20
χ472-2-222-22-220-20-202000002-22-200−i2i2−i2i22-22-200002-20000−i2i2−i2i2−i2i20000−i2i2−i2i20000000000−i2i20
χ482-2-222-22-220-20-202000002-22-200−i2i2−i2i2-22-220000-220000−i2i2−i2i2−i2i20000i2−i2i2−i20000000000i2−i20
χ492-2-222-22-220-20-20200000-22-2200i2−i2i2−i22-22-20000-220000−i2i2−i2i2i2−i20000i2−i2i2−i20000000000−i2i20
χ502-2-222-22-220-20-20200000-22-2200i2−i2i2−i2-22-2200002-20000−i2i2−i2i2i2−i20000−i2i2−i2i20000000000i2−i20
χ512-2-222-22-220-20-20200000-22-2200−i2i2−i2i22-22-20000-220000i2−i2i2−i2−i2i20000−i2i2−i2i20000000000i2−i20
χ522-2-222-22-220-20-20200000-22-2200−i2i2−i2i2-22-2200002-20000i2−i2i2−i2−i2i20000i2−i2i2−i20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-4-44-404040-40-4000000000000002222−22−2200000000−2222000000000000000000000000000
χ55444-4-4-44-404040-40-400000000000000−22−2222220000000022−22000000000000000000000000000
χ5644-44-4-4-444040-40-40000000000000000000000000000022−22−222200000000000000000000000
χ5744-44-4-4-444040-40-400000000000000000000000000000−222222−2200000000000000000000000
χ5844-44-4-4-44-40-40404000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ5944-44-4-4-44-40-4040400000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ604-444-44-4-444-4-444-4-4000000004-4000000000000000000000000000000000000000000000
χ614-44-44-4-44040-40-4044i−4i−4i4i000000000000000000000000000000000000000000000000000
χ624-44-44-4-44040-40-404−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ634-44-44-4-440-404040-400000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ644-44-44-4-440-404040-40000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ654-4-444-44-4-404040-4000000000002i2−2i22i2−2i2000000000000000000−2i22i2000000000000000000000
χ664-4-444-44-4-404040-400000000000−2i22i2−2i22i20000000000000000002i2−2i2000000000000000000000
χ674-4-4-4-444400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ684-4-4-4-444400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ694-4-4-4-4444000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ704-4-4-4-4444000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ7188-8-888-8-8000000000000000000000000000000000000000000000000000000000000000

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