Finite Group Databasebeta

← Group #10868289

Character table — Group #10868289

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order1222222234444666666644121212122444444668888121224242424242424244444444444412121212121212124444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-111-1-1-1-1111-1-111-1-1-1-1-1
χ41111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-111-1-111111
χ5111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11111-1-1111-1-1-1-1-1-11
χ6111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-11111-1-1-1-1-1111111-1
χ7111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1
χ8111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ911111111111111111111-1-11111-111-1-111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-11111-1-1-1-11-1-1-1-111-1-11
χ1011111111111111111111-1-11111-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-11111-1-1-1-1-11111-1-111-1
χ1111111111111111111111-1-11111-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1111-1-111-1-1111-1-1-1-111-1
χ1211111111111111111111-1-11111-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-111111-1-111-1-1-1-1-11111-1-11
χ1311111111111111111111-1-11111-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111-1-1111
χ1411111111111111111111-1-11111-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111111111-1-1-111-1-111-111-1-111-1-1-1
χ1511111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111111111-1-1-1
χ1611111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1111
χ17222222222-2-2-2-2222222222-2-2-2-2-2000000-2-20000220000000022-2-2000022000000000-2000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2000000-2-200002200000000-2-2220000-2-20000000002000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-22000000220000-2-20000000022220000-2-2000000000-2000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-22000000220000-2-200000000-2-2-2-20000220000000002000000000
χ2122222222-12222-1-1-1-1-1-1-122-1-1-1-12222222-1-12222-1-1-1-1-1-1-1-1-1-100000000002-1-1-1-1-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-122222-2-2-1-1-2-2-2-2-1-1111111110000000000-2-1-11111-1-10000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-12-2-2-2-222-1-1-2-2-2-2-1-1111111110000000000211-1-1-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-122-1-1-1-12-2-2-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-10000000000-2111111110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-222-2-2221122-2-211-1-1-1-111110000000000-2-1-1-1-111110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-222-2-2-2-211-2-222111111-1-1-1-100000000002-1-111-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2222211-2-222111111-1-1-1-10000000000-211-1-111-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-222-2-21122-2-211-1-1-1-11111000000000021111-1-1-1-10000000000
χ2922-22-22-2-222-2-22-2-2-222-22002-22-202-200000000000000000000002i−2i00002i−2i02-20000000002i−2i00000
χ3022-22-22-2-222-2-22-2-2-222-22002-22-202-20000000000000000000000−2i2i0000−2i2i02-2000000000−2i2i00000
χ3122-22-22-2-222-2-22-2-2-222-22002-22-20-2200000000000000000000002i−2i00002i−2i0-22000000000−2i2i00000
χ3222-22-22-2-222-2-22-2-2-222-22002-22-20-220000000000000000000000−2i2i0000−2i2i0-220000000002i−2i00000
χ3322-22-22-2-22-222-2-2-2-222-2200-22-220002-2000000000000000000002i−2i2i2i−2i−2i−2i2i00000002-20000000000
χ3422-22-22-2-22-222-2-2-2-222-2200-22-220002-200000000000000000000−2i2i−2i−2i2i2i2i−2i00000002-20000000000
χ3522-22-22-2-22-222-2-2-2-222-2200-22-22000-22000000000000000000002i−2i−2i−2i2i2i−2i2i0000000-220000000000
χ3622-22-22-2-22-222-2-2-2-222-2200-22-22000-2200000000000000000000−2i2i2i2i−2i−2i2i−2i0000000-220000000000
χ372-2222-2-2-22-22-222-2-2-2-22200-2-222000000000002-200000022-2-200002i−2i2i−2i0000000000002i−2i0000000
χ382-2222-2-2-22-22-222-2-2-2-22200-2-222000000000002-200000022-2-20000−2i2i−2i2i000000000000−2i2i0000000
χ392-2222-2-2-22-22-222-2-2-2-22200-2-22200000000000-22000000-2-22200002i−2i2i−2i000000000000−2i2i0000000
χ402-2222-2-2-22-22-222-2-2-2-22200-2-22200000000000-22000000-2-2220000−2i2i−2i2i0000000000002i−2i0000000
χ412-2-22-2-222222-2-2-222-2-2-22002-2-22000002i−2i000000000000000000002-2-22000002i−2i0000000002i−2i000
χ422-2-22-2-222222-2-2-222-2-2-22002-2-22000002i−2i00000000000000000000-222-2000002i−2i000000000−2i2i000
χ432-2-22-2-222222-2-2-222-2-2-22002-2-2200000−2i2i000000000000000000002-2-2200000−2i2i000000000−2i2i000
χ442-2-22-2-222222-2-2-222-2-2-22002-2-2200000−2i2i00000000000000000000-222-200000−2i2i0000000002i−2i000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-2442222-4000000220000-2-20000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-422224000000-2-20000220000000000000000000000000000000000000
χ47444-4-4-44-44000044-44-4-4-4000000000000000000000000000004-4000000000000000000000000000
χ48444-4-4-44-44000044-44-4-4-400000000000000000000000000000-44000000000000000000000000000
χ4944-44-44-4-4-24-4-44222-2-22-200-22-2204-40000000000000000000000000000000-220000000000000000
χ5044-44-44-4-4-24-4-44222-2-22-200-22-220-4400000000000000000000000000000002-20000000000000000
χ5144-44-44-4-4-2-444-4222-2-22-2002-22-20004-400000000000000000000000000000000000-220000000000
χ5244-44-44-4-4-2-444-4222-2-22-2002-22-2000-44000000000000000000000000000000000002-20000000000
χ5344-4-44-4-4440000-4-444-44-44i−4i000000000000000004i−4i0000000000000000000000000000000000000
χ5444-4-44-4-4440000-4-444-44-4−4i4i00000000000000000−4i4i0000000000000000000000000000000000000
χ5544-4-44-4-44-2000022-2-22-224i−4i00000000000000000−2i2ii6i6−i6−i66−66−600000000000000000000000000000
χ5644-4-44-4-44-2000022-2-22-224i−4i00000000000000000−2i2i−i6−i6i6i6−66−6600000000000000000000000000000
χ5744-4-44-4-44-2000022-2-22-22−4i4i000000000000000002i−2ii6i6−i6−i6−66−6600000000000000000000000000000
χ5844-4-44-4-44-2000022-2-22-22−4i4i000000000000000002i−2i−i6−i6i6i66−66−600000000000000000000000000000
χ594-4444-4-4-444-44-44-4-4-4-4440044-4-40000000000000000000000000000000000000000000000000000
χ604-4444-4-4-4-24-44-4-22222-2-200-2-22200000000000000023−2323−23000000000000000000000000000000000
χ614-4444-4-4-4-24-44-4-22222-2-200-2-222000000000000000−2323−2323000000000000000000000000000000000
χ624-4444-4-4-4-2-44-44-22222-2-20022-2-2000000000004-4000000-2-22200000000000000000000000000000
χ634-4444-4-4-4-2-44-44-22222-2-20022-2-200000000000-4400000022-2-200000000000000000000000000000
χ644-44-4-44-44400004-44-44-4-40000000000000000000000000000000000000000000000000000000−2i22i20
χ654-44-4-44-44400004-44-44-4-400000000000000000000000000000000000000000000000000000002i2−2i20
χ664-4-44-4-4444-4-444-444-4-4-4400-444-40000000000000000000000000000000000000000000000000000
χ674-4-44-4-444-244-4-42-2-2222-200-222-2000004i−4i00000000000000000000000000000−2i2i00000000000000
χ684-4-44-4-444-244-4-42-2-2222-200-222-200000−4i4i000000000000000000000000000002i−2i00000000000000
χ694-4-44-4-444-2-4-4442-2-2222-2002-2-220000000000000000000000000000000000000023−23000000000000
χ704-4-44-4-444-2-4-4442-2-2222-2002-2-2200000000000000000000000000000000000000−2323000000000000
χ714-4-4-4444-440000-44-4-444-4000000000000000−2i22i20000−2i22i22i2−2i2000000000000000000000000000000000
χ724-4-4-4444-440000-44-4-444-40000000000000002i2−2i200002i2−2i2−2i22i2000000000000000000000000000000000
χ734-4-4-4444-4-200002-222-2-220000000000000−2i32i3−2i22i20000i2−i2−i2i26−6−6600000000000000000000000000000
χ744-4-4-4444-4-200002-222-2-220000000000000−2i32i32i2−2i20000−i2i2i2−i2−666−600000000000000000000000000000
χ754-4-4-4444-4-200002-222-2-2200000000000002i3−2i3−2i22i20000i2−i2−i2i2−666−600000000000000000000000000000
χ764-4-4-4444-4-200002-222-2-2200000000000002i3−2i32i2−2i20000−i2i2i2−i26−6−6600000000000000000000000000000
χ77888-8-8-88-8-40000-4-44-44440000000000000000000000000000000000000000000000000000000000
χ788-88-8-88-88-40000-44-44-4440000000000000000000000000000000000000000000000000000000000

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