Finite Group Databasebeta

← Group #10868244

Character table — Group #10868244

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order12222222344446666666441212121222244446688881212242424242424242444444444444661212121212124444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-11111-1-1-1-11-1-111-1-1-1-1-1
χ411111111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-111111
χ5111111111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-11
χ6111111111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-11111-1-1-1111111-1
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
χ911111111111111111111-1-11111-11111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1-11-1-111-1-1111
χ1011111111111111111111-1-11111-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-111-1-111-1-1-111-1-111-1-1-1
χ1111111111111111111111-1-11111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1
χ1211111111111111111111-1-11111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111111111-1-1-1-111-1-1-1-1-1-1-1111
χ1311111111111111111111-1-11111-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-11111-1-11-1-1-1-111-1-11
χ1411111111111111111111-1-11111-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-11111-1-1-11111-1-111-1
χ1511111111111111111111-1-11111-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-11-1-111-1-111111-1-1-1-111-1
χ1611111111111111111111-1-11111-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111-1-111-1-111-1-1-11111-1-11
χ17222222222-2-2-2-2222222222-2-2-2-2-2000000-2-20000220000000022220000-2-2000000000-2000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2000000-2-200002200000000-2-2-2-20000220000000002000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-22000000220000-2-20000000022-2-2000022000000000-2000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-22000000220000-2-200000000-2-2220000-2-20000000002000000000
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
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-1222-2-222-1-1-2-2-2-2-1-1111111110000000000-2-1-1-1-111110000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-12-2-222-2-2-1-1-2-2-2-2-1-111111111000000000021111-1-1-1-10000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-22222-2-211-2-22211-1-1-1-111110000000000-2-1-111-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-222-2-2-2-21122-2-2111111-1-1-1-100000000002-1-11111-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-222221122-2-2111111-1-1-1-10000000000-211-1-1-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2-2-22211-2-22211-1-1-1-111110000000000211-1-111-1-10000000000
χ29222-2-22-2-222-2-22-2-2-2222-2002-22-2000002-20000000000000000002i−2i00002i−2i0002-200000002i−2i00000
χ30222-2-22-2-222-2-22-2-2-2222-2002-22-2000002-2000000000000000000−2i2i0000−2i2i0002-20000000−2i2i00000
χ31222-2-22-2-222-2-22-2-2-2222-2002-22-200000-220000000000000000002i−2i00002i−2i000-220000000−2i2i00000
χ32222-2-22-2-222-2-22-2-2-2222-2002-22-200000-22000000000000000000−2i2i0000−2i2i000-2200000002i−2i00000
χ33222-2-22-2-22-222-2-2-2-2222-200-22-2202-200000000000000000000002i−2i2i2i−2i−2i−2i2i02-20000000000000000
χ34222-2-22-2-22-222-2-2-2-2222-200-22-2202-20000000000000000000000−2i2i−2i−2i2i2i2i−2i02-20000000000000000
χ35222-2-22-2-22-222-2-2-2-2222-200-22-220-2200000000000000000000002i−2i−2i−2i2i2i−2i2i0-220000000000000000
χ36222-2-22-2-22-222-2-2-2-2222-200-22-220-220000000000000000000000−2i2i2i2i−2i−2i2i−2i0-220000000000000000
χ3722-222-2-2-22-22-222-2-22-2-2200-2-222000000000002-20022-2-2000000002i−2i2i−2i0000000000002i−2i0000000
χ3822-222-2-2-22-22-222-2-22-2-2200-2-222000000000002-20022-2-200000000−2i2i−2i2i000000000000−2i2i0000000
χ3922-222-2-2-22-22-222-2-22-2-2200-2-22200000000000-2200-2-222000000002i−2i2i−2i000000000000−2i2i0000000
χ4022-222-2-2-22-22-222-2-22-2-2200-2-22200000000000-2200-2-22200000000−2i2i−2i2i0000000000002i−2i0000000
χ4122-2-2-2-222222-2-2-2222-2-2-2002-2-220002i−2i00000000000000000000002-2-2200000002i−2i00000002i−2i000
χ4222-2-2-2-222222-2-2-2222-2-2-2002-2-220002i−2i0000000000000000000000-222-200000002i−2i0000000−2i2i000
χ4322-2-2-2-222222-2-2-2222-2-2-2002-2-22000−2i2i00000000000000000000002-2-220000000−2i2i0000000−2i2i000
χ4422-2-2-2-222222-2-2-2222-2-2-2002-2-22000−2i2i0000000000000000000000-222-20000000−2i2i00000002i−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
χ47444-4-44-4-4-24-4-44222-2-2-2200-22-22000004-400000000000000000000000000000-2200000000000000
χ48444-4-44-4-4-24-4-44222-2-2-2200-22-2200000-44000000000000000000000000000002-200000000000000
χ49444-4-44-4-4-2-444-4222-2-2-22002-22-204-40000000000000000000000000000000-220000000000000000
χ50444-4-44-4-4-2-444-4222-2-2-22002-22-20-4400000000000000000000000000000002-20000000000000000
χ5144-444-4-4-444-44-44-4-44-4-440044-4-40000000000000000000000000000000000000000000000000000
χ5244-444-4-4-4-24-44-4-222-222-200-2-22200000000000000000002323−23−2300000000000000000000000000000
χ5344-444-4-4-4-24-44-4-222-222-200-2-2220000000000000000000−23−23232300000000000000000000000000000
χ5444-444-4-4-4-2-44-44-222-222-20022-2-2000000000004-400-2-222000000000000000000000000000000000
χ5544-444-4-4-4-2-44-44-222-222-20022-2-200000000000-440022-2-2000000000000000000000000000000000
χ5644-4-4-4-4444-4-444-4444-4-4-400-444-40000000000000000000000000000000000000000000000000000
χ5744-4-4-4-444-244-4-42-2-2-222200-222-20004i−4i000000000000000000000000000000000−2i2i000000000000
χ5844-4-4-4-444-244-4-42-2-2-222200-222-2000−4i4i0000000000000000000000000000000002i−2i000000000000
χ5944-4-4-4-444-2-4-4442-2-2-2222002-2-22000000000000000000000000000000000000000023−230000000000
χ6044-4-4-4-444-2-4-4442-2-2-2222002-2-220000000000000000000000000000000000000000−23230000000000
χ614-444-4-4-444000044-4-44-4-44i−4i000000000000000004i−4i0000000000000000000000000000000000000
χ624-444-4-4-444000044-4-44-4-4−4i4i00000000000000000−4i4i0000000000000000000000000000000000000
χ634-444-4-4-44-20000-2-222-2224i−4i00000000000000000−2i2i6−66−6i6−i6i6−i600000000000000000000000000000
χ644-444-4-4-44-20000-2-222-2224i−4i00000000000000000−2i2i−66−66−i6i6−i6i600000000000000000000000000000
χ654-444-4-4-44-20000-2-222-222−4i4i000000000000000002i−2i6−66−6−i6i6−i6i600000000000000000000000000000
χ664-444-4-4-44-20000-2-222-222−4i4i000000000000000002i−2i−66−66i6−i6i6−i600000000000000000000000000000
χ674-44-44-44-440000-4-44-44-44000000000000000000000000000004i−4i000000000000000000000000000
χ684-44-44-44-440000-4-44-44-4400000000000000000000000000000−4i4i000000000000000000000000000
χ694-4-44-444-4400004-44-4-44-4000000000000000−2i22i200000000−2i22i22i2−2i200000000000000000000000000000
χ704-4-44-444-4400004-44-4-44-40000000000000002i2−2i2000000002i2−2i2−2i22i200000000000000000000000000000
χ714-4-44-444-4-20000-22-222-220000000000000−2i32i3−2i22i200006−6−66i2−i2−i2i200000000000000000000000000000
χ724-4-44-444-4-20000-22-222-220000000000000−2i32i32i2−2i20000−666−6−i2i2i2−i200000000000000000000000000000
χ734-4-44-444-4-20000-22-222-2200000000000002i3−2i3−2i22i20000−666−6i2−i2−i2i200000000000000000000000000000
χ744-4-44-444-4-20000-22-222-2200000000000002i3−2i32i2−2i200006−6−66−i2i2i2−i200000000000000000000000000000
χ754-4-4-444-4440000-44-4-4-444000000000000000000000000000000000000000000000000000000022−220
χ764-4-4-444-4440000-44-4-4-4440000000000000000000000000000000000000000000000000000000−22220
χ778-88-88-88-8-4000044-44-44-40000000000000000000000000000000000000000000000000000000000
χ788-8-8-888-88-400004-4444-4-40000000000000000000000000000000000000000000000000000000000

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