Finite Group Databasebeta

← Group #10844644

Character table — Group #10844644

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order1222222234444666666644121212122244444888812121212242424242424242444444444444661212121212124444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-111-1-11-1-111-1-1-1-11
χ411111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-111-1-1-111-1-11111-1
χ511111111111111111111111111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-111-1-111111-1-1-1-1-1-1-1
χ611111111111111111111111111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11111111
χ711111111111111111111111111-1-11-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1
χ811111111111111111111111111-1-11-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ911111111111111111111-1-1111111-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-111-1-11
χ1011111111111111111111-1-1111111-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-111-1-1-1-111-1-1-111-1-111-1
χ1111111111111111111111-1-1111111-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-11111-1-1-1-11-1-1-1-1-1-1111
χ1211111111111111111111-1-1111111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11111-1-1-1-1-1111111-1-1-1
χ1311111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-111-1
χ1411111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111111111-1-1-1-11111-1-1-1-1-111-1-11
χ1511111111111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11-1-11111-1-11-1-11111-1-1-1
χ1611111111111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-111-1-1-1-1111
χ17222222222-2-2-2-2222222222-2-2-2-200-200000000-2-2220000000022000022-2-2000000000-2000000000
χ18222222222-2-2-2-2222222222-2-2-2-200-200000000-2-22200000000-2-20000-2-2220000000002000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-20020000000022-2-200000000220000-2-222000000000-2000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-20020000000022-2-200000000-2-2000022-2-20000000002000000000
χ2122222222-12222-1-1-1-1-1-1-122-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-100000000002-1-1-1-1-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-11111111100000000002-1-111-1-1110000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-222222-2-2-2-2-1-1-1-1111111110000000000-211-1-111-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-22-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000000000-2111111110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-222-2-222-2-21111-1-1-1-111110000000000-2-1-11111-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-2-222-2-22211111111-1-1-1-10000000000-2-1-1-1-111110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-222-2-2-2-22211111111-1-1-1-1000000000021111-1-1-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2-2-22222-2-21111-1-1-1-111110000000000211-1-1-1-1110000000000
χ2922-22-22-2-222-2-2222-2-2-22-2002-22-200000002i−2i0000002i2i−2i−2i00000022-2-200000000000000002i−2i00000
χ3022-22-22-2-222-2-2222-2-2-22-2002-22-200000002i−2i0000002i2i−2i−2i000000-2-2220000000000000000−2i2i00000
χ3122-22-22-2-222-2-2222-2-2-22-2002-22-20000000−2i2i000000−2i−2i2i2i00000022-2-20000000000000000−2i2i00000
χ3222-22-22-2-222-2-2222-2-2-22-2002-22-20000000−2i2i000000−2i−2i2i2i000000-2-22200000000000000002i−2i00000
χ332-22-222-2-222-22-2-2-2-22-222002-2-222-2000000000000000000000002i−2i2i−2i000002-200000000000002i−2i0
χ342-22-222-2-222-22-2-2-2-22-222002-2-222-200000000000000000000000−2i2i−2i2i000002-20000000000000−2i2i0
χ352-22-222-2-222-22-2-2-2-22-222002-2-22-22000000000000000000000002i−2i2i−2i00000-220000000000000−2i2i0
χ362-22-222-2-222-22-2-2-2-22-222002-2-22-2200000000000000000000000−2i2i−2i2i00000-2200000000000002i−2i0
χ372-2-2-2-2222222-2-2-2-22-222-20022-2-20002i−2i000000000000000000002i−2i−2i2i2-22-200000002i−2i0000000000
χ382-2-2-2-2222222-2-2-2-22-222-20022-2-20002i−2i00000000000000000000−2i2i2i−2i-22-2200000002i−2i0000000000
χ392-2-2-2-2222222-2-2-2-22-222-20022-2-2000−2i2i000000000000000000002i−2i−2i2i-22-220000000−2i2i0000000000
χ402-2-2-2-2222222-2-2-2-22-222-20022-2-2000−2i2i00000000000000000000−2i2i2i−2i2-22-20000000−2i2i0000000000
χ412-2-2-2-22222-2-222-2-22-222-200-2-222000002-200000000000000000000002-2-220002-2000002-20000000
χ422-2-2-2-22222-2-222-2-22-222-200-2-222000002-20000000000000000000000-222-20002-200000-220000000
χ432-2-2-2-22222-2-222-2-22-222-200-2-22200000-2200000000000000000000002-2-22000-2200000-220000000
χ442-2-2-2-22222-2-222-2-22-222-200-2-22200000-220000000000000000000000-222-2000-22000002-20000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-244222200-40000000022-2-20000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4222200400000000-2-2220000000000000000000000000000000000000
χ47444-4-4-44-4400004-444-4-4-40000000000000000000000000000000000000000000000000000022−22000
χ48444-4-4-44-4400004-444-4-4-400000000000000000000000000000000000000000000000000000−2222000
χ4944-44-44-4-44-444-444-4-4-44-400-44-440000000000000000000000000000000000000000000000000000
χ5044-44-44-4-4-24-4-44-2-2222-2200-22-2200000004i−4i000000−2i−2i2i2i000000000000000000000000000000000
χ5144-44-44-4-4-24-4-44-2-2222-2200-22-220000000−4i4i0000002i2i−2i−2i000000000000000000000000000000000
χ5244-44-44-4-4-2-444-4-2-2222-22002-22-200000000000000000002323−23−2300000000000000000000000000000
χ5344-44-44-4-4-2-444-4-2-2222-22002-22-20000000000000000000−23−23232300000000000000000000000000000
χ5444-4-44-4-44400004-4-4-44-44000000000000000000000000000004i−4i000000000000000000000000000
χ5544-4-44-4-44400004-4-4-44-4400000000000000000000000000000−4i4i000000000000000000000000000
χ564-444-4-4-4440000-44-444-4-44i−4i000000000000000004i−4i0000000000000000000000000000000000000
χ574-444-4-4-4440000-44-444-4-4−4i4i00000000000000000−4i4i0000000000000000000000000000000000000
χ584-444-4-4-44-200002-22-2-2224i−4i00000000000000000−2i2i6−66−6i6−i6i6−i600000000000000000000000000000
χ594-444-4-4-44-200002-22-2-2224i−4i00000000000000000−2i2i−66−66−i6i6−i6i600000000000000000000000000000
χ604-444-4-4-44-200002-22-2-222−4i4i000000000000000002i−2i6−66−6−i6i6−i6i600000000000000000000000000000
χ614-444-4-4-44-200002-22-2-222−4i4i000000000000000002i−2i−66−66i6−i6i6−i600000000000000000000000000000
χ624-44-444-4-44-44-44-4-4-44-44400-444-40000000000000000000000000000000000000000000000000000
χ634-44-444-4-4-24-44-4222-22-2-200-222-24-400000000000000000000000000000000-220000000000000000
χ644-44-444-4-4-24-44-4222-22-2-200-222-2-44000000000000000000000000000000002-20000000000000000
χ654-44-444-4-4-2-44-44222-22-2-2002-2-2200000000000000000000000000000000000000−2i32i3000000000000
χ664-44-444-4-4-2-44-44222-22-2-2002-2-22000000000000000000000000000000000000002i3−2i3000000000000
χ674-4-444-44-440000-444-4-4-44000000000000000−2i22i200000000−2i22i22i2−2i200000000000000000000000000000
χ684-4-444-44-440000-444-4-4-440000000000000002i2−2i2000000002i2−2i2−2i22i200000000000000000000000000000
χ694-4-444-44-4-200002-2-2222-2000000000000000−2i22i223−2300i6−i6−i6i6i2−i2−i2i200000000000000000000000000000
χ704-4-444-44-4-200002-2-2222-2000000000000000−2i22i2−232300−i6i6i6−i6i2−i2−i2i200000000000000000000000000000
χ714-4-444-44-4-200002-2-2222-20000000000000002i2−2i223−2300−i6i6i6−i6−i2i2i2−i200000000000000000000000000000
χ724-4-444-44-4-200002-2-2222-20000000000000002i2−2i2−232300i6−i6−i6i6−i2i2i2−i200000000000000000000000000000
χ734-4-4-4-4444-244-4-422-22-2-2200-2-2220004i−4i00000000000000000000000000000000000−2i2i0000000000
χ744-4-4-4-4444-244-4-422-22-2-2200-2-222000−4i4i000000000000000000000000000000000002i−2i0000000000
χ754-4-4-4-4444-2-4-44422-22-2-220022-2-2000004-400000000000000000000000000000-2200000000000000
χ764-4-4-4-4444-2-4-44422-22-2-220022-2-200000-44000000000000000000000000000002-200000000000000
χ77888-8-8-88-8-40000-44-4-44440000000000000000000000000000000000000000000000000000000000
χ7888-8-88-8-88-40000-4444-44-40000000000000000000000000000000000000000000000000000000000

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