Finite Group Databasebeta

← Group #10875954

Character table — Group #10875954

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order1222222234444666666644121212124444444888812121212242424242424242422224444442661212121212124444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-111-1-11111-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-11-1-111-1-1-1-11
χ5111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-11111111-1-1-1-1-1-1-1
χ6111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111111
χ7111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ8111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1
χ911111111111111111111-1-11111-11111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-111-1-111-1
χ1011111111111111111111-1-11111-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1111-1-111-1-11
χ1111111111111111111111-1-11111-111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-111-1-1111-1-1-1-1-1-1111
χ1211111111111111111111-1-11111-111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-111-1111111-1-1-1
χ1311111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1111-1-111-1-1-1-1-1-1-111-1-11
χ1411111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-111111-1-111-1
χ1511111111111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-1-1111-1-11111-1-1-1
χ1611111111111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-1-1-111-111-1-1-1-1111
χ17222222222-2-2-2-2222222222-2-2-2-2-2000000000022-2-200000000000022-2-2-2-20000000002000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2000000000022-2-2000000000000-2-22222000000000-2000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-220000000000-2-22200000000000022-2-222000000000-2000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-220000000000-2-222000000000000-2-222-2-20000000002000000000
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
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-11111111100000000002-1-1-1-111110000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-12-2-22222-2-2-2-2-1-1-1-1111111110000000000-21111-1-1-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-122-1-1-1-12-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000000000-2111111110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-22222-2-222-2-21111-1-1-1-111110000000000-211-1-1-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-222-2-222-2-22211111111-1-1-1-10000000000-211-1-111-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-222-2-2-2-22211111111-1-1-1-100000000002-1-111-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2-2-22222-2-21111-1-1-1-1111100000000002-1-11111-1-10000000000
χ29222-2-22-2-22-2-2222-22-2-22-2002-22-200000002i−2i0000002i2i−2i−2i000022-2-20000000000000000002i−2i00000
χ30222-2-22-2-22-2-2222-22-2-22-2002-22-200000002i−2i0000002i2i−2i−2i0000-2-222000000000000000000−2i2i00000
χ31222-2-22-2-22-2-2222-22-2-22-2002-22-20000000−2i2i000000−2i−2i2i2i000022-2-2000000000000000000−2i2i00000
χ32222-2-22-2-22-2-2222-22-2-22-2002-22-20000000−2i2i000000−2i−2i2i2i0000-2-2220000000000000000002i−2i00000
χ332-222-2-2-2222-2-22-2-2222-2-200-222-2000002i−2i000000000000000000002i−2i2i−2i0000000002i−2i02-20000000
χ342-222-2-2-2222-2-22-2-2222-2-200-222-2000002i−2i00000000000000000000−2i2i−2i2i0000000002i−2i0-220000000
χ352-222-2-2-2222-2-22-2-2222-2-200-222-200000−2i2i000000000000000000002i−2i2i−2i000000000−2i2i0-220000000
χ362-222-2-2-2222-2-22-2-2222-2-200-222-200000−2i2i00000000000000000000−2i2i−2i2i000000000−2i2i02-20000000
χ372-222-2-2-222-222-2-2-2222-2-2002-2-220002i−2i0000000000000000002-22-22i−2i−2i2i00000002i−2i000000000000
χ382-222-2-2-222-222-2-2-2222-2-2002-2-220002i−2i000000000000000000-22-22−2i2i2i−2i00000002i−2i000000000000
χ392-222-2-2-222-222-2-2-2222-2-2002-2-22000−2i2i0000000000000000002-22-2−2i2i2i−2i0000000−2i2i000000000000
χ402-222-2-2-222-222-2-2-2222-2-2002-2-22000−2i2i000000000000000000-22-222i−2i−2i2i0000000−2i2i000000000000
χ412-22-22-22-222-22-2-222-2-2-220022-2-202i−2i000000000000000000002-2-220000000002i−2i000000000002i−2i0
χ422-22-22-22-222-22-2-222-2-2-220022-2-202i−2i00000000000000000000-222-20000000002i−2i00000000000−2i2i0
χ432-22-22-22-222-22-2-222-2-2-220022-2-20−2i2i000000000000000000002-2-22000000000−2i2i00000000000−2i2i0
χ442-22-22-22-222-22-2-222-2-2-220022-2-20−2i2i00000000000000000000-222-2000000000−2i2i000000000002i−2i0
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-2442222-40000000000-2-2220000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-422224000000000022-2-20000000000000000000000000000000000000
χ47444-4-44-4-4444-4-44-44-4-44-400-44-440000000000000000000000000000000000000000000000000000
χ48444-4-44-4-4-244-4-4-22-222-22002-22-200000000000000000002323−23−2300000000000000000000000000000
χ49444-4-44-4-4-244-4-4-22-222-22002-22-20000000000000000000−23−23232300000000000000000000000000000
χ50444-4-44-4-4-2-4-444-22-222-2200-22-2200000004i−4i000000−2i−2i2i2i000000000000000000000000000000000
χ51444-4-44-4-4-2-4-444-22-222-2200-22-220000000−4i4i0000002i2i−2i−2i000000000000000000000000000000000
χ5244-444-4-4-44000044-44-4-4-40000000000000000000000000000000000000000000000000000022−22000
χ5344-444-4-4-44000044-44-4-4-400000000000000000000000000000000000000000000000000000−2222000
χ5444-4-4-4-444400004-4-4-44-4400000000000000000000000000000000000004-40000000000000000000
χ5544-4-4-4-444400004-4-4-44-440000000000000000000000000000000000000-440000000000000000000
χ564-444-4-4-44-24-4-4422-2-2-222002-2-22000004i−4i000000000000000000000000000000000−2i2i0000000000
χ574-444-4-4-44-24-4-4422-2-2-222002-2-2200000−4i4i0000000000000000000000000000000002i−2i0000000000
χ584-444-4-4-44-2-444-422-2-2-22200-222-20004i−4i000000000000000000000000000000000−2i2i000000000000
χ594-444-4-4-44-2-444-422-2-2-22200-222-2000−4i4i0000000000000000000000000000000002i−2i000000000000
χ604-44-44-44-44-44-44-444-4-4-4400-4-4440000000000000000000000000000000000000000000000000000
χ614-44-44-44-4-24-44-42-2-2222-200-2-22204i−4i000000000000000000000000000000000−2i2i00000000000000
χ624-44-44-44-4-24-44-42-2-2222-200-2-2220−4i4i0000000000000000000000000000000002i−2i00000000000000
χ634-44-44-44-4-2-44-442-2-2222-20022-2-20000000000000000000000000000000000−2i32i30000000000000000
χ644-44-44-44-4-2-44-442-2-2222-20022-2-200000000000000000000000000000000002i3−2i30000000000000000
χ654-4-44-444-440000-4-4-44-44400000000000000022−220000000022−2222−2200000000000000000000000000000
χ664-4-44-444-440000-4-4-44-444000000000000000−222200000000−2222−222200000000000000000000000000000
χ674-4-44-444-4-20000222-22-2-200000000000000022−2200−2i32i3i6−i6i6−i6−22−2200000000000000000000000000000
χ684-4-44-444-4-20000222-22-2-200000000000000022−22002i3−2i3−i6i6−i6i6−22−2200000000000000000000000000000
χ694-4-44-444-4-20000222-22-2-2000000000000000−222200−2i32i3−i6i6−i6i62−22−200000000000000000000000000000
χ704-4-44-444-4-20000222-22-2-2000000000000000−2222002i3−2i3i6−i6i6−i62−22−200000000000000000000000000000
χ714-4-4-444-4440000-44-4-444-44-40000000000000004-4000000000000000000000000000000000000000
χ724-4-4-444-4440000-44-4-444-4-44000000000000000-44000000000000000000000000000000000000000
χ734-4-4-444-44-200002-222-2-224-4000000000000000-22006−6−666−6−6600000000000000000000000000000
χ744-4-4-444-44-200002-222-2-224-4000000000000000-2200−666−6−666−600000000000000000000000000000
χ754-4-4-444-44-200002-222-2-22-440000000000000002-2006−6−66−666−600000000000000000000000000000
χ764-4-4-444-44-200002-222-2-22-440000000000000002-200−666−66−6−6600000000000000000000000000000
χ7788-888-8-8-8-40000-4-44-44440000000000000000000000000000000000000000000000000000000000
χ7888-8-8-8-888-40000-4444-44-40000000000000000000000000000000000000000000000000000000000

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