Finite Group Databasebeta

← Group #10855112

Character table — Group #10855112

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
χ31111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-11111-1-1-1-1111-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111111
χ5111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-11111-1-1111-1-1-1-11
χ6111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-1-11111-1
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
χ911111111111111111111-1-11111-111-1-111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-111-1-111-1-111-11111-1-1-1
χ1011111111111111111111-1-11111-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-11111-111-1-111-1-1-1-11-1-1-1-1111
χ1111111111111111111111-1-11111-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1111
χ1211111111111111111111-1-11111-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-11111111-1-1-1-111-1-111111-1-1-1
χ1311111111111111111111-1-11111-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1111111-1-1-11111-1-1-1-1-111-1-111-1
χ1411111111111111111111-1-11111-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-11111-1-1111-1-111-1-11
χ1511111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111111-1-111-1-111-1-1-1-1-111-1-11
χ1611111111111111111111-1-11111-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11-1-111-1-11111111-1-111-1
χ17222222222-2-2-2-2222222222-2-2-2-2-2000000-2-20000220000000022-2-2-2-200000000000000020000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2000000-2-200002200000000-2-22222000000000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-122222-2-2-1-1-2-2-2-2-1-1111111110000000000-2-1-1-1-111110000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-12-2-2-2-222-1-1-2-2-2-2-1-111111111000000000021111-1-1-1-10000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-222-2-2221122-2-211-1-1-1-111110000000000-2-1-111-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-222-2-2-2-211-2-222111111-1-1-1-100000000002-1-11111-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-2222211-2-222111111-1-1-1-10000000000-211-1-1-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-2-2-222-2-21122-2-211-1-1-1-111110000000000211-1-111-1-10000000000
χ29222-22-2-2-22-22-222-2-22-2-2200-2-222000000000002-200000022-2-20000002i2i−2i−2i0000000000002i−2i00000
χ30222-22-2-2-22-22-222-2-22-2-2200-2-222000000000002-200000022-2-2000000−2i−2i2i2i000000000000−2i2i00000
χ31222-22-2-2-22-22-222-2-22-2-2200-2-22200000000000-22000000-2-2220000002i2i−2i−2i000000000000−2i2i00000
χ32222-22-2-2-22-22-222-2-22-2-2200-2-22200000000000-22000000-2-222000000−2i−2i2i2i0000000000002i−2i00000
χ332-2-222-22-222-2-22-222-2-2-22002-22-20002i−2i0000000000000000002-2002-22i−2i2i−2i0002i−2i00000000000000
χ342-2-222-22-222-2-22-222-2-2-22002-22-20002i−2i000000000000000000-2200-22−2i2i−2i2i0002i−2i00000000000000
χ352-2-222-22-222-2-22-222-2-2-22002-22-2000−2i2i0000000000000000002-2002-2−2i2i−2i2i000−2i2i00000000000000
χ362-2-222-22-222-2-22-222-2-2-22002-22-2000−2i2i000000000000000000-2200-222i−2i2i−2i000−2i2i00000000000000
χ372-2-222-22-22-222-2-222-2-2-2200-22-2202i−2i000000000000000000002-200-22000002i−2i0000002i−2i00000000
χ382-2-222-22-22-222-2-222-2-2-2200-22-2202i−2i00000000000000000000-22002-2000002i−2i000000−2i2i00000000
χ392-2-222-22-22-222-2-222-2-2-2200-22-220−2i2i000000000000000000002-200-2200000−2i2i000000−2i2i00000000
χ402-2-222-22-22-222-2-222-2-2-2200-22-220−2i2i00000000000000000000-22002-200000−2i2i0000002i−2i00000000
χ412-2-2-222-222-2-222-2-2-2-222200-222-2000002-200000000000000000000002-2-22000002-20000000002-20
χ422-2-2-222-222-2-222-2-2-2-222200-222-2000002-20000000000000000000000-222-2000002-2000000000-220
χ432-2-2-222-222-2-222-2-2-2-222200-222-200000-2200000000000000000000002-2-2200000-22000000000-220
χ442-2-2-222-222-2-222-2-2-2-222200-222-200000-220000000000000000000000-222-200000-220000000002-20
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
χ47444-44-4-4-444-44-44-4-44-4-440044-4-40000000000000000000000000000000000000000000000000000
χ48444-44-4-4-4-24-44-4-222-222-200-2-2220000000000000002323−23−23000000000000000000000000000000000
χ49444-44-4-4-4-24-44-4-222-222-200-2-222000000000000000−23−232323000000000000000000000000000000000
χ50444-44-4-4-4-2-44-44-222-222-20022-2-2000000000004-4000000-2-22200000000000000000000000000000
χ51444-44-4-4-4-2-44-44-222-222-20022-2-200000000000-4400000022-2-200000000000000000000000000000
χ5244-44-44-4-44000044-4-44-4-400000000000000000000000000000004-40000000000000000000000000
χ5344-44-44-4-44000044-4-44-4-40000000000000000000000000000000-440000000000000000000000000
χ5444-4-4-4-444400004-44-4-44-400000000000000000000000000000000000000000000000000000−2i22i2000
χ5544-4-4-4-444400004-44-4-44-4000000000000000000000000000000000000000000000000000002i2−2i2000
χ564-444-4-4-4440000-44-44-44-44i−4i000000000000000004i−4i0000000000000000000000000000000000000
χ574-444-4-4-4440000-44-44-44-4−4i4i00000000000000000−4i4i0000000000000000000000000000000000000
χ584-444-4-4-44-200002-22-22-224i−4i00000000000000000−2i2ii6−i6i6−i66−66−600000000000000000000000000000
χ594-444-4-4-44-200002-22-22-224i−4i00000000000000000−2i2i−i6i6−i6i6−66−6600000000000000000000000000000
χ604-444-4-4-44-200002-22-22-22−4i4i000000000000000002i−2ii6−i6i6−i6−66−6600000000000000000000000000000
χ614-444-4-4-44-200002-22-22-22−4i4i000000000000000002i−2i−i6i6−i6i66−66−600000000000000000000000000000
χ624-44-4-444-440000-4-4444-4-4000000000000000−2i22i20000−2i22i22i2−2i2000000000000000000000000000000000
χ634-44-4-444-440000-4-4444-4-40000000000000002i2−2i200002i2−2i2−2i22i2000000000000000000000000000000000
χ644-44-4-444-4-2000022-2-2-2220000000000000−2i32i3−2i22i20000i2−i2−i2i26−6−6600000000000000000000000000000
χ654-44-4-444-4-2000022-2-2-2220000000000000−2i32i32i2−2i20000−i2i2i2−i2−666−600000000000000000000000000000
χ664-44-4-444-4-2000022-2-2-22200000000000002i3−2i3−2i22i20000i2−i2−i2i2−666−600000000000000000000000000000
χ674-44-4-444-4-2000022-2-2-22200000000000002i3−2i32i2−2i20000−i2i2i2−i26−6−6600000000000000000000000000000
χ684-4-444-44-4-24-4-442-2-2222-200-22-220004i−4i0000000000000000000000000000000−2i2i00000000000000
χ694-4-444-44-4-24-4-442-2-2222-200-22-22000−4i4i00000000000000000000000000000002i−2i00000000000000
χ704-4-444-44-4-2-444-42-2-2222-2002-22-204i−4i0000000000000000000000000000000−2i2i0000000000000000
χ714-4-444-44-4-2-444-42-2-2222-2002-22-20−4i4i00000000000000000000000000000002i−2i0000000000000000
χ724-4-4-444-44444-4-4-4-4-4-4444004-4-440000000000000000000000000000000000000000000000000000
χ734-4-4-444-44-244-4-42222-2-2-200-222-20000000000000000000000000000000000000000−2i32i30000000000
χ744-4-4-444-44-244-4-42222-2-2-200-222-200000000000000000000000000000000000000002i3−2i30000000000
χ754-4-4-444-44-2-4-4442222-2-2-2002-2-22000004-40000000000000000000000000000000-22000000000000
χ764-4-4-444-44-2-4-4442222-2-2-2002-2-2200000-4400000000000000000000000000000002-2000000000000
χ7788-88-88-8-8-40000-4-444-4440000000000000000000000000000000000000000000000000000000000
χ7888-8-8-8-888-40000-44-444-440000000000000000000000000000000000000000000000000000000000

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