Finite Group Databasebeta

← Group #10840255

Character table — Group #10840255

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444888888888888888888888881212121212121212121216161616161616161624242424242424242448
order1222222234444666666644121212122444444668888121224242424242424242244444444412121212121212124444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-111-1-1-1-1111-1-1-1-11
χ411111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-111-1-1-11111-1
χ5111111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-111-1-111111-1-1-1-1-1-1-1
χ6111111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11111111
χ7111111111111111111111111111-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1
χ8111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-1-1-11
χ911111111111111111111-1-11111-11111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-11111-1-1-1-1-1-11-1-111-1-11
χ1011111111111111111111-1-11111-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-111-111-1-111-1
χ1111111111111111111111-1-11111-111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1111
χ1211111111111111111111-1-11111-111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111111111-111-1-1-1-111-1-1-11111-1-1-1
χ1311111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-11111-1-1-1-1111-1-111-1
χ1411111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-1-11111-1-111-1-1-111-1-11
χ1511111111111111111111-1-11111-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111111111-1-1-1
χ1611111111111111111111-1-11111-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1111
χ17222222222-2-2-2-2222222222-2-2-2-2-2000000-2-20000220000000022-2-222000000000000000-20000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2000000-2-200002200000000-2-222-2-200000000000000020000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-22000000220000-2-2000000002222-2-2000000000000000-20000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-22000000220000-2-200000000-2-2-2-22200000000000000020000000
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
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-1222-2-2-2-2-1-1-2-2-2-2-1-11111111100000000002-1-111-1-1110000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-12-2-22222-1-1-2-2-2-2-1-1111111110000000000-211-1-111-1-10000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-22222-2-211-2-22211-1-1-1-111110000000000-2-1-1-1-111110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-222-2-2221122-2-2111111-1-1-1-10000000000-2-1-11111-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-222-2-21122-2-2111111-1-1-1-10000000000211-1-1-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2-2-22211-2-22211-1-1-1-11111000000000021111-1-1-1-10000000000
χ2922-2-2-2-22222-22-22-2-22-2-220022-2-20000000002i−2i000000002i2i−2i−2i0000002i2i−2i−2i0000000000002-200000
χ3022-2-2-2-22222-22-22-2-22-2-220022-2-20000000002i−2i000000002i2i−2i−2i000000−2i−2i2i2i000000000000-2200000
χ3122-2-2-2-22222-22-22-2-22-2-220022-2-2000000000−2i2i00000000−2i−2i2i2i0000002i2i−2i−2i000000000000-2200000
χ3222-2-2-2-22222-22-22-2-22-2-220022-2-2000000000−2i2i00000000−2i−2i2i2i000000−2i−2i2i2i0000000000002-200000
χ332-222-2-2-2222-2-22-22-222-2-2002-22-2000002i−2i0000000000000000002-22-22i−2i2i−2i00000002i−2i0000000000
χ342-222-2-2-2222-2-22-22-222-2-2002-22-2000002i−2i000000000000000000-22-22−2i2i−2i2i00000002i−2i0000000000
χ352-222-2-2-2222-2-22-22-222-2-2002-22-200000−2i2i0000000000000000002-22-2−2i2i−2i2i0000000−2i2i0000000000
χ362-222-2-2-2222-2-22-22-222-2-2002-22-200000−2i2i000000000000000000-22-222i−2i2i−2i0000000−2i2i0000000000
χ372-222-2-2-222-222-2-22-222-2-200-22-220002i−2i000000000000000000002-2-2200000002i−2i00002i−2i00000000
χ382-222-2-2-222-222-2-22-222-2-200-22-220002i−2i00000000000000000000-222-200000002i−2i0000−2i2i00000000
χ392-222-2-2-222-222-2-22-222-2-200-22-22000−2i2i000000000000000000002-2-220000000−2i2i0000−2i2i00000000
χ402-222-2-2-222-222-2-22-222-2-200-22-22000−2i2i00000000000000000000-222-20000000−2i2i00002i−2i00000000
χ412-2-2-222-22222-2-2-2-222-22-2002-2-2202i−2i000000000000000000000000002-2-2202i−2i000000000002i−2i000
χ422-2-2-222-22222-2-2-2-222-22-2002-2-2202i−2i00000000000000000000000000-222-202i−2i00000000000−2i2i000
χ432-2-2-222-22222-2-2-2-222-22-2002-2-220−2i2i000000000000000000000000002-2-220−2i2i00000000000−2i2i000
χ442-2-2-222-22222-2-2-2-222-22-2002-2-220−2i2i00000000000000000000000000-222-20−2i2i000000000002i−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
χ47444-4-44-4-44000044-4-4-44-4000000000000000000000000000004-4000000000000000000000000000
χ48444-4-44-4-44000044-4-4-44-400000000000000000000000000000-44000000000000000000000000000
χ4944-444-4-4-4400004-44-44-4-4000000000000000000000000000000000000000000000000000000022−220
χ5044-444-4-4-4400004-44-44-4-40000000000000000000000000000000000000000000000000000000−22220
χ5144-4-4-4-4444-44-444-4-44-4-4400-4-4440000000000000000000000000000000000000000000000000000
χ5244-4-4-4-444-24-44-4-222-222-200-2-2220000000004i−4i00000000−2i−2i2i2i00000000000000000000000000000
χ5344-4-4-4-444-24-44-4-222-222-200-2-222000000000−4i4i000000002i2i−2i−2i00000000000000000000000000000
χ5444-4-4-4-444-2-44-44-222-222-20022-2-2000000000000000−2i3−2i32i32i3000000000000000000000000000000000
χ5544-4-4-4-444-2-44-44-222-222-20022-2-20000000000000002i32i3−2i3−2i3000000000000000000000000000000000
χ564-444-4-4-44-24-4-442-22-2-22200-22-22000004i−4i000000000000000000000000000000000−2i2i0000000000
χ574-444-4-4-44-24-4-442-22-2-22200-22-2200000−4i4i0000000000000000000000000000000002i−2i0000000000
χ584-444-4-4-44-2-444-42-22-2-222002-22-20004i−4i0000000000000000000000000000000−2i2i00000000000000
χ594-444-4-4-44-2-444-42-22-2-222002-22-2000−4i4i00000000000000000000000000000002i−2i00000000000000
χ604-44-44-44-440000-444-4-4-444i−4i000000000000000004i−4i0000000000000000000000000000000000000
χ614-44-44-44-440000-444-4-4-44−4i4i00000000000000000−4i4i0000000000000000000000000000000000000
χ624-44-44-44-4-200002-2-2222-24i−4i00000000000000000−2i2ii6−i6i6−i66−66−600000000000000000000000000000
χ634-44-44-44-4-200002-2-2222-24i−4i00000000000000000−2i2i−i6i6−i6i6−66−6600000000000000000000000000000
χ644-44-44-44-4-200002-2-2222-2−4i4i000000000000000002i−2ii6−i6i6−i6−66−6600000000000000000000000000000
χ654-44-44-44-4-200002-2-2222-2−4i4i000000000000000002i−2i−i6i6−i6i66−66−600000000000000000000000000000
χ664-4-44-444-440000-4-4-4-44440000000000000000022−220022−22−2222000000000000000000000000000000000
χ674-4-44-444-440000-4-4-4-444400000000000000000−222200−222222−22000000000000000000000000000000000
χ684-4-44-444-4-200002222-2-2-20000000000000−2i32i30022−2200−222−2i6−i6−i6i600000000000000000000000000000
χ694-4-44-444-4-200002222-2-2-20000000000000−2i32i300−2222002−2−22−i6i6i6−i600000000000000000000000000000
χ704-4-44-444-4-200002222-2-2-200000000000002i3−2i30022−2200−222−2−i6i6i6−i600000000000000000000000000000
χ714-4-44-444-4-200002222-2-2-200000000000002i3−2i300−2222002−2−22i6−i6−i6i600000000000000000000000000000
χ724-4-4-444-444-4-444-4-444-44-400-444-40000000000000000000000000000000000000000000000000000
χ734-4-4-444-44-244-4-422-2-22-2200-222-204i−4i0000000000000000000000000000000−2i2i0000000000000000
χ744-4-4-444-44-244-4-422-2-22-2200-222-20−4i4i00000000000000000000000000000002i−2i0000000000000000
χ754-4-4-444-44-2-4-44422-2-22-22002-2-220000000000000000000000000000000000000023−23000000000000
χ764-4-4-444-44-2-4-44422-2-22-22002-2-2200000000000000000000000000000000000000−2323000000000000
χ77888-8-88-8-8-40000-4-4444-440000000000000000000000000000000000000000000000000000000000
χ7888-888-8-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000

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