Finite Group Databasebeta

← Group #10868304

Character table — Group #10868304

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
χ31111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-11111-1-11-1-111-1-1-1-1-1
χ41111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-111111
χ5111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-11
χ6111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1111111-1
χ7111111111111111111111111111-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1
χ8111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ911111111111111111111-1-11111-111-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-11111-1-1-1-11-1-1-1-111-1-11
χ1011111111111111111111-1-11111-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-1-11111-1-111-1
χ1111111111111111111111-1-11111-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-1-111-1-111111-1-1-1-111-1
χ1211111111111111111111-1-11111-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-111-1-111-1-1-11111-1-11
χ1311111111111111111111-1-11111-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-111-1-11-1-111-1-1111
χ1411111111111111111111-1-11111-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111111111-111-1-111-1-1-111-1-111-1-1-1
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
χ17222222222-2-2-2-2222222222-2-2-2-2-2000000-2-2000022000000002222-2-20000000000000-2000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2000000-2-200002200000000-2-2-2-22200000000000002000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-22000000220000-2-20000000022-2-2220000000000000-2000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-22000000220000-2-200000000-2-222-2-200000000000002000000000
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
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-122222-2-2-1-1-2-2-2-2-1-1111111110000000000-211-1-1-1-1110000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-12-2-2-2-222-1-1-2-2-2-2-1-11111111100000000002-1-11111-1-10000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-222-2-2221122-2-211-1-1-1-111110000000000-2-1-1-1-111110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-222-2-2-2-211-2-222111111-1-1-1-10000000000211-1-111-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2222211-2-222111111-1-1-1-10000000000-2-1-111-1-1110000000000
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
χ29222-22-2-2-22-22-222-2-2-222-200-2-222000000000002-200000022-2-20000002i2i−2i−2i00000000002i−2i0000000
χ30222-22-2-2-22-22-222-2-2-222-200-2-222000000000002-200000022-2-2000000−2i−2i2i2i0000000000−2i2i0000000
χ31222-22-2-2-22-22-222-2-2-222-200-2-22200000000000-22000000-2-2220000002i2i−2i−2i0000000000−2i2i0000000
χ32222-22-2-2-22-22-222-2-2-222-200-2-22200000000000-22000000-2-222000000−2i−2i2i2i00000000002i−2i0000000
χ332-222-22-2-222-2-22-22-2-2-222002-22-202-200000000000000000000002i−2i2i−2i00000002-200000002i−2i00000
χ342-222-22-2-222-2-22-22-2-2-222002-22-202-20000000000000000000000−2i2i−2i2i00000002-20000000−2i2i00000
χ352-222-22-2-222-2-22-22-2-2-222002-22-20-2200000000000000000000002i−2i2i−2i0000000-220000000−2i2i00000
χ362-222-22-2-222-2-22-22-2-2-222002-22-20-220000000000000000000000−2i2i−2i2i0000000-2200000002i−2i00000
χ372-222-22-2-22-222-2-22-2-2-22200-22-220002-2000000000000000000002i−2i−2i2i2i−2i2i−2i000002-2000000000000
χ382-222-22-2-22-222-2-22-2-2-22200-22-220002-200000000000000000000−2i2i2i−2i−2i2i−2i2i000002-2000000000000
χ392-222-22-2-22-222-2-22-2-2-22200-22-22000-22000000000000000000002i−2i−2i2i−2i2i−2i2i00000-22000000000000
χ402-222-22-2-22-222-2-22-2-2-22200-22-22000-2200000000000000000000−2i2i2i−2i2i−2i2i−2i00000-22000000000000
χ412-22-2-2-222222-2-2-2-222-22-2002-2-22000002i−2i00000000000000000000002-2-2202i−2i000000000002i−2i000
χ422-22-2-2-222222-2-2-2-222-22-2002-2-22000002i−2i0000000000000000000000-222-202i−2i00000000000−2i2i000
χ432-22-2-2-222222-2-2-2-222-22-2002-2-2200000−2i2i00000000000000000000002-2-220−2i2i00000000000−2i2i000
χ442-22-2-2-222222-2-2-2-222-22-2002-2-2200000−2i2i0000000000000000000000-222-20−2i2i000000000002i−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
χ47444-44-4-4-444-44-44-4-4-444-40044-4-40000000000000000000000000000000000000000000000000000
χ48444-44-4-4-4-24-44-4-2222-2-2200-2-2220000000000000002323−23−23000000000000000000000000000000000
χ49444-44-4-4-4-24-44-4-2222-2-2200-2-222000000000000000−23−232323000000000000000000000000000000000
χ50444-44-4-4-4-2-44-44-2222-2-220022-2-2000000000004-4000000-2-22200000000000000000000000000000
χ51444-44-4-4-4-2-44-44-2222-2-220022-2-200000000000-4400000022-2-200000000000000000000000000000
χ5244-44-4-4-44400004-44-4-4-444i−4i000000000000000004i−4i0000000000000000000000000000000000000
χ5344-44-4-4-44400004-44-4-4-44−4i4i00000000000000000−4i4i0000000000000000000000000000000000000
χ5444-44-4-4-44-20000-22-2222-24i−4i00000000000000000−2i2i6−66−6i6−i6i6−i600000000000000000000000000000
χ5544-44-4-4-44-20000-22-2222-24i−4i00000000000000000−2i2i−66−66−i6i6−i6i600000000000000000000000000000
χ5644-44-4-4-44-20000-22-2222-2−4i4i000000000000000002i−2i6−66−6−i6i6−i6i600000000000000000000000000000
χ5744-44-4-4-44-20000-22-2222-2−4i4i000000000000000002i−2i−66−66i6−i6i6−i600000000000000000000000000000
χ5844-4-4-444-44000044-44-4-4-400000000000000022−22000022−22−2222000000000000000000000000000000000
χ5944-4-4-444-44000044-44-4-4-4000000000000000−22220000−222222−22000000000000000000000000000000000
χ6044-4-4-444-4-20000-2-22-22220000000000000−2i32i322−220000−222−2i6−i6−i6i600000000000000000000000000000
χ6144-4-4-444-4-20000-2-22-22220000000000000−2i32i3−222200002−2−22−i6i6i6−i600000000000000000000000000000
χ6244-4-4-444-4-20000-2-22-222200000000000002i3−2i322−220000−222−2−i6i6i6−i600000000000000000000000000000
χ6344-4-4-444-4-20000-2-22-222200000000000002i3−2i3−222200002−2−22i6−i6−i6i600000000000000000000000000000
χ644-444-44-4-4-24-4-442-2222-2-200-22-2204-4000000000000000000000000000000000-2200000000000000
χ654-444-44-4-4-24-4-442-2222-2-200-22-220-440000000000000000000000000000000002-200000000000000
χ664-444-44-4-4-2-444-42-2222-2-2002-22-20004-4000000000000000000000000000000000-22000000000000
χ674-444-44-4-4-2-444-42-2222-2-2002-22-2000-440000000000000000000000000000000002-2000000000000
χ684-44-4-4-4444-4-444-4-444-44-400-444-40000000000000000000000000000000000000000000000000000
χ694-44-4-4-444-244-4-422-2-22-2200-222-2000004i−4i000000000000000000000000000−2i2i0000000000000000
χ704-44-4-4-444-244-4-422-2-22-2200-222-200000−4i4i0000000000000000000000000002i−2i0000000000000000
χ714-44-4-4-444-2-4-44422-2-22-22002-2-22000000000000000000000000000000000000000023−230000000000
χ724-44-4-4-444-2-4-44422-2-22-22002-2-220000000000000000000000000000000000000000−23230000000000
χ734-4-444-44-440000-4-4-444-44000000000000000000000000000004i−4i000000000000000000000000000
χ744-4-444-44-440000-4-4-444-4400000000000000000000000000000−4i4i000000000000000000000000000
χ754-4-4-444-4440000-444-44-4-40000000000000000000000000000000000000000000000000000000−2i22i20
χ764-4-4-444-4440000-444-44-4-400000000000000000000000000000000000000000000000000000002i2−2i20
χ778-8-888-88-8-40000444-4-44-40000000000000000000000000000000000000000000000000000000000
χ788-8-8-888-88-400004-4-44-4440000000000000000000000000000000000000000000000000000000000

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