Finite Group Databasebeta

← Group #10853235

Character table — Group #10853235

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order122222223444466666664412121212444444488881212121224242424242424242244444444412121212121212124444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-111-1-111-1-1-1-1111-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-111111
χ511111111111111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-111-1-111111-1-1-1-1-1-11
χ611111111111111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-111-1-1-1111111-1
χ711111111111111111111111111-1-11-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1
χ811111111111111111111111111-1-11-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-1-1-11
χ911111111111111111111-1-1111111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-111-1-1-1-11111-1-1-1-1-111-1
χ1011111111111111111111-1-1111111-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-111-1-111111-1-11
χ1111111111111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111111111-1-1-1-1-1-1-1-1-111-1-11
χ1211111111111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111-1-1-1-111111-1-111-1
χ1311111111111111111111-1-11111-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1
χ1411111111111111111111-1-11111-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-11111-1-11-1-1-1-1111
χ1511111111111111111111-1-11111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-1-11111-1-1-1-1-111-1-1111
χ1611111111111111111111-1-11111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-11111-1-1111-1-111-1-1-1
χ17222222222-2-2-2-2222222222-2-2-2-200-20000000022-2-20000000022-2-222000000000000000-20000000
χ18222222222-2-2-2-2222222222-2-2-2-200-20000000022-2-200000000-2-222-2-200000000000000020000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-200200000000-2-2220000000022-2-2-2-200000000000000020000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-200200000000-2-22200000000-2-22222000000000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-122222-2-2-2-2-2-2-1-1-1-1111111110000000000-2-1-111-1-1110000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-22-2-222-2-2-2-2-1-1-1-1111111110000000000211-1-111-1-10000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-2-22222-2-21111-1-1-1-111110000000000-2-1-11111-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-122-2-2-2-2-2-2-22211111111-1-1-1-100000000002-1-1-1-111110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-22222-2-22211111111-1-1-1-10000000000-21111-1-1-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-222-2-222-2-21111-1-1-1-111110000000000211-1-1-1-1110000000000
χ29222-2-22-2-2222-2-22-22-22-2-20022-2-22-20000000000000000000002-22-20022-2-202-20000000000000000
χ30222-2-22-2-2222-2-22-22-22-2-20022-2-22-2000000000000000000000-22-2200-2-22202-20000000000000000
χ31222-2-22-2-2222-2-22-22-22-2-20022-2-2-220000000000000000000002-22-200-2-2220-220000000000000000
χ32222-2-22-2-2222-2-22-22-22-2-20022-2-2-22000000000000000000000-22-220022-2-20-220000000000000000
χ33222-2-22-2-22-2-2222-22-22-2-200-2-2220002i−2i0000000000000000002-2-22000000000002i−2i000002i−2i00000
χ34222-2-22-2-22-2-2222-22-22-2-200-2-2220002i−2i000000000000000000-222-2000000000002i−2i00000−2i2i00000
χ35222-2-22-2-22-2-2222-22-22-2-200-2-222000−2i2i0000000000000000002-2-2200000000000−2i2i00000−2i2i00000
χ36222-2-22-2-22-2-2222-22-22-2-200-2-222000−2i2i000000000000000000-222-200000000000−2i2i000002i−2i00000
χ372-222-2-22-222-2-22-222-2-22-2002-2-22000002i−2i00000000000000000000002i−2i2i−2i00000002i−2i00000002-20
χ382-222-2-22-222-2-22-222-2-22-2002-2-22000002i−2i0000000000000000000000−2i2i−2i2i00000002i−2i0000000-220
χ392-222-2-22-222-2-22-222-2-22-2002-2-2200000−2i2i00000000000000000000002i−2i2i−2i0000000−2i2i0000000-220
χ402-222-2-22-222-2-22-222-2-22-2002-2-2200000−2i2i0000000000000000000000−2i2i−2i2i0000000−2i2i00000002-20
χ412-22-22-2-2222-22-2-2-222-2-22002-22-200000002i−2i0000002i2i−2i−2i00000000002i−2i−2i2i0000000002-200000000
χ422-22-22-2-2222-22-2-2-222-2-22002-22-200000002i−2i0000002i2i−2i−2i0000000000−2i2i2i−2i000000000-2200000000
χ432-22-22-2-2222-22-2-2-222-2-22002-22-20000000−2i2i000000−2i−2i2i2i00000000002i−2i−2i2i000000000-2200000000
χ442-22-22-2-2222-22-2-2-222-2-22002-22-20000000−2i2i000000−2i−2i2i2i0000000000−2i2i2i−2i0000000002-200000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-244222200-400000000-2-2220000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-422220040000000022-2-20000000000000000000000000000000000000
χ47444-4-44-4-4-244-4-4-22-22-22200-2-2224-400000000000000000000000000000000-220000000000000000
χ48444-4-44-4-4-244-4-4-22-22-22200-2-222-44000000000000000000000000000000002-20000000000000000
χ49444-4-44-4-4-2-4-444-22-22-2220022-2-20004i−4i000000000000000000000000000000000−2i2i000000000000
χ50444-4-44-4-4-2-4-444-22-22-2220022-2-2000−4i4i0000000000000000000000000000000002i−2i000000000000
χ5144-444-4-4-4400004-4-44-44-40000000000000000000000000000000004-400000000000000000000000
χ5244-444-4-4-4400004-4-44-44-4000000000000000000000000000000000-4400000000000000000000000
χ5344-4-4-4-4444000044-4-4-4-444i−4i0000000000000004i−4i000000000000000000000000000000000000000
χ5444-4-4-4-4444000044-4-4-4-44−4i4i000000000000000−4i4i000000000000000000000000000000000000000
χ5544-4-4-4-444-20000-2-22222-24i−4i000000000000000−2i2i006−66−6i6i6−i6−i600000000000000000000000000000
χ5644-4-4-4-444-20000-2-22222-24i−4i000000000000000−2i2i00−66−66−i6−i6i6i600000000000000000000000000000
χ5744-4-4-4-444-20000-2-22222-2−4i4i0000000000000002i−2i006−66−6−i6−i6i6i600000000000000000000000000000
χ5844-4-4-4-444-20000-2-22222-2−4i4i0000000000000002i−2i00−66−66i6i6−i6−i600000000000000000000000000000
χ594-444-4-44-44-444-4-444-4-44-400-444-40000000000000000000000000000000000000000000000000000
χ604-444-4-44-4-24-4-442-2-222-2200-222-2000004i−4i000000000000000000000000000000000−2i2i0000000000
χ614-444-4-44-4-24-4-442-2-222-2200-222-200000−4i4i0000000000000000000000000000000002i−2i0000000000
χ624-444-4-44-4-2-444-42-2-222-22002-2-22000000000000000000000000000000000000−2i32i300000000000000
χ634-444-4-44-4-2-444-42-2-222-22002-2-220000000000000000000000000000000000002i3−2i300000000000000
χ644-44-44-4-444-44-44-4-444-4-4400-44-440000000000000000000000000000000000000000000000000000
χ654-44-44-4-44-24-44-422-2-222-200-22-2200000004i−4i000000−2i−2i2i2i000000000000000000000000000000000
χ664-44-44-4-44-24-44-422-2-222-200-22-220000000−4i4i0000002i2i−2i−2i000000000000000000000000000000000
χ674-44-44-4-44-2-44-4422-2-222-2002-22-20000000000000000000−2i32i3−2i32i300000000000000000000000000000
χ684-44-44-4-44-2-44-4422-2-222-2002-22-200000000000000000002i3−2i32i3−2i300000000000000000000000000000
χ694-4-44-44-4440000-4-4-4-444400000000000000022−220000000022−22−222200000000000000000000000000000
χ704-4-44-44-4440000-4-4-4-4444000000000000000−222200000000−222222−2200000000000000000000000000000
χ714-4-44-44-44-200002222-2-2-200000000000000022−2200−2i32i3i6−i6−i6i6−222−200000000000000000000000000000
χ724-4-44-44-44-200002222-2-2-200000000000000022−22002i3−2i3−i6i6i6−i6−222−200000000000000000000000000000
χ734-4-44-44-44-200002222-2-2-2000000000000000−222200−2i32i3−i6i6i6−i62−2−2200000000000000000000000000000
χ744-4-44-44-44-200002222-2-2-2000000000000000−2222002i3−2i3i6−i6−i6i62−2−2200000000000000000000000000000
χ754-4-4-4444-440000-44-444-4-400000000000000000000000000000000000000000000000000000−2i22i2000
χ764-4-4-4444-440000-44-444-4-4000000000000000000000000000000000000000000000000000002i2−2i2000
χ7788-888-8-8-8-40000-444-44-440000000000000000000000000000000000000000000000000000000000
χ788-8-8-8888-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000

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