Finite Group Databasebeta

← Group #10858396

Character table — Group #10858396

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
χ31111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111-1-1-111-1-11111-1
χ41111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-11-1-111-1-1-1-11
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
χ711111111111111111111111111-1-1-1-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ811111111111111111111111111-1-1-1-11-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1
χ911111111111111111111-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-11111-1-1-1-11-1-1-1-111-1-11
χ1011111111111111111111-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-11111-1-1-1-1-11111-1-111-1
χ1111111111111111111111-1-1111111-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-111-111-1-1-1-111-1-1-11111-1-1-1
χ1211111111111111111111-1-1111111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-1-1-111111-1-1-1-1111
χ1311111111111111111111-1-11111-1-111-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-11-1-11111-1-11-1-111-1-111-1
χ1411111111111111111111-1-11111-1-111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111-1-11111-1-1-111-1-111-1-11
χ1511111111111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1111
χ1611111111111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-111111111111-1-1-1
χ17222222222-2-2-2-2222222222-2-2-2-20000-200000022-2-20000000000002222-2-2000000000-2000000000
χ18222222222-2-2-2-2222222222-2-2-2-20000-200000022-2-2000000000000-2-2-2-2220000000002000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-200002000000-2-22200000000000022-2-2-2-20000000002000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-200002000000-2-222000000000000-2-22222000000000-2000000000
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
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-122-2-22-2-2-2-2-2-2-1-1-1-11111111100000000002-1-111-1-1110000000000
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
χ2422222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-22-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000000000-2111111110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-12222-2-2-222-2-21111-1-1-1-111110000000000-2-1-1-1-111110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-2-222-2-22211111111-1-1-1-10000000000-2-1-11111-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-222-2-2-2-2-22211111111-1-1-1-10000000000211-1-1-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2-2-22222-2-21111-1-1-1-11111000000000021111-1-1-1-10000000000
χ29222-22-2-2-222-22-2222-2-2-2-20022-2-22-200000000000000000000022-2-200000002-2000000000002-2000
χ30222-22-2-2-222-22-2222-2-2-2-20022-2-22-2000000000000000000000-2-22200000002-200000000000-22000
χ31222-22-2-2-222-22-2222-2-2-2-20022-2-2-2200000000000000000000022-2-20000000-2200000000000-22000
χ32222-22-2-2-222-22-2222-2-2-2-20022-2-2-22000000000000000000000-2-2220000000-22000000000002-2000
χ332-2-222-22-222-2-22-2-2222-2-2002-22-2002i−2i000000000000000000000002i−2i002i−2i0002i−2i000002-20000000
χ342-2-222-22-222-2-22-2-2222-2-2002-22-2002i−2i00000000000000000000000−2i2i00−2i2i0002i−2i00000-220000000
χ352-2-222-22-222-2-22-2-2222-2-2002-22-200−2i2i000000000000000000000002i−2i002i−2i000−2i2i00000-220000000
χ362-2-222-22-222-2-22-2-2222-2-2002-22-200−2i2i00000000000000000000000−2i2i00−2i2i000−2i2i000002-20000000
χ372-2-222-22-22-222-2-2-2222-2-200-22-22000002i−2i00000000000000002-22-22i−2i00−2i2i00000002i−2i0000000000
χ382-2-222-22-22-222-2-2-2222-2-200-22-22000002i−2i0000000000000000-22-22−2i2i002i−2i00000002i−2i0000000000
χ392-2-222-22-22-222-2-2-2222-2-200-22-2200000−2i2i00000000000000002-22-2−2i2i002i−2i0000000−2i2i0000000000
χ402-2-222-22-22-222-2-2-2222-2-200-22-2200000−2i2i0000000000000000-22-222i−2i00−2i2i0000000−2i2i0000000000
χ412-2-2-222-222-2-222-2-22-2-22200-222-20000000002-20000000022-2-22-2-220000000000000000002-200000
χ422-2-2-222-222-2-222-2-22-2-22200-222-20000000002-20000000022-2-2-222-2000000000000000000-2200000
χ432-2-2-222-222-2-222-2-22-2-22200-222-2000000000-2200000000-2-2222-2-22000000000000000000-2200000
χ442-2-2-222-222-2-222-2-22-2-22200-222-2000000000-2200000000-2-222-222-20000000000000000002-200000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-24422220000-4000000-2-2220000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-422220000400000022-2-20000000000000000000000000000000000000
χ47444-44-4-4-44-44-44444-4-4-4-400-4-4440000000000000000000000000000000000000000000000000000
χ48444-44-4-4-4-24-44-4-2-2-2222200-2-2224-400000000000000000000000000000000-220000000000000000
χ49444-44-4-4-4-24-44-4-2-2-2222200-2-222-44000000000000000000000000000000002-20000000000000000
χ50444-44-4-4-4-2-44-44-2-2-222220022-2-20000000000000000000000000000000000000023−23000000000000
χ51444-44-4-4-4-2-44-44-2-2-222220022-2-200000000000000000000000000000000000000−2323000000000000
χ5244-44-44-4-4400004-4-44-44-4000000000000022−220000002222−22−22000000000000000000000000000000000
χ5344-44-44-4-4400004-4-44-44-40000000000000−2222000000−22−222222000000000000000000000000000000000
χ5444-44-44-4-4-20000-222-22-22000000000000022−22000023−23−2−2226−66−600000000000000000000000000000
χ5544-44-44-4-4-20000-222-22-22000000000000022−220000−2323−2−222−66−6600000000000000000000000000000
χ5644-44-44-4-4-20000-222-22-220000000000000−2222000023−2322−2−2−66−6600000000000000000000000000000
χ5744-44-44-4-4-20000-222-22-220000000000000−22220000−232322−2−26−66−600000000000000000000000000000
χ5844-4-4-4-444400004-4-4-44-44000000000000000000000000000000000004-4000000000000000000000
χ5944-4-4-4-444400004-4-4-44-4400000000000000000000000000000000000-44000000000000000000000
χ604-444-4-4-4440000-44-44-4-440000000000000000000000000000000000000000000000000000000−2i22i20
χ614-444-4-4-4440000-44-44-4-4400000000000000000000000000000000000000000000000000000002i2−2i20
χ624-44-4-444-440000-44-4-444-44i−4i0000000000000004i−4i000000000000000000000000000000000000000
χ634-44-4-444-440000-44-4-444-4−4i4i000000000000000−4i4i000000000000000000000000000000000000000
χ644-44-4-444-4-200002-222-2-224i−4i000000000000000−2i2i00i6−i6i6−i66−6−6600000000000000000000000000000
χ654-44-4-444-4-200002-222-2-224i−4i000000000000000−2i2i00−i6i6−i6i6−666−600000000000000000000000000000
χ664-44-4-444-4-200002-222-2-22−4i4i0000000000000002i−2i00i6−i6i6−i6−666−600000000000000000000000000000
χ674-44-4-444-4-200002-222-2-22−4i4i0000000000000002i−2i00−i6i6−i6i66−6−6600000000000000000000000000000
χ684-4-444-44-4-24-4-4422-2-2-22200-22-22004i−4i00000000000000000000000000000000−2i2i00000000000000
χ694-4-444-44-4-24-4-4422-2-2-22200-22-2200−4i4i000000000000000000000000000000002i−2i00000000000000
χ704-4-444-44-4-2-444-422-2-2-222002-22-2000004i−4i000000000000000000000000000000000−2i2i0000000000
χ714-4-444-44-4-2-444-422-2-2-222002-22-200000−4i4i0000000000000000000000000000000002i−2i0000000000
χ724-4-4-444-44444-4-4-4-44-4-444004-4-440000000000000000000000000000000000000000000000000000
χ734-4-4-444-44-244-4-422-222-2-200-222-2000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ744-4-4-444-44-244-4-422-222-2-200-222-20000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ754-4-4-444-44-2-4-44422-222-2-2002-2-220000000004-400000000-2-22200000000000000000000000000000
χ764-4-4-444-44-2-4-44422-222-2-2002-2-22000000000-440000000022-2-200000000000000000000000000000
χ7788-8-8-8-888-40000-4444-44-40000000000000000000000000000000000000000000000000000000000
χ788-888-8-8-88-400004-44-444-40000000000000000000000000000000000000000000000000000000000

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