Finite Group Databasebeta

← Group #10845539

Character table — Group #10845539

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222224444444488888888888888888888121212121212121212121212161616161616161616162424242424244848
order1222222234444666666622441212121244446688881212242424242424242444448888888844121212121212121224444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1111-1
χ4111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-111111-1-1-1-1-1-111-1-1-11
χ51111111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-111111111-1-1-11
χ61111111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-11111-1-1-1-1111-1
χ71111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ911111111111111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1
χ1011111111111111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-1-111
χ1111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111111-111-1-1-1-111-1-1-1-111-11
χ1211111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-1-1-1111111-1-11-1
χ1311111111111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-11-1-11111-1-1-1-111-1-11-1
χ1411111111111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-11111-1-111-1-111-11
χ1511111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-111
χ1611111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111111111-1-1
χ17222222222-2-2-2-2222222222-2-2-2-2-2-20000220000-2-20000000022-2-20000000000000000002-2000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-20000220000-2-200000000-2-222000000000000000000-22000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-20000-2-20000220000000022-2-2000000000000000000-22000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-20000-2-200002200000000-2-2220000000000000000002-2000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1-1-1-1-100000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-122-2-2-1-1-2-2-2-2-1-111111111000000000000-22-1-1-1-1111100000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-222-1-1-2-2-2-2-1-1111111110000000000002-21111-1-1-1-100000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-1000000000000-2-21111111100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122221122-2-211-1-1-1-11111000000000000-2-2-1-111-1-11100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-211-2-222111111-1-1-1-10000000000002-2-1-11111-1-100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211-2-222111111-1-1-1-1000000000000-2211-1-1-1-11100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-2-2-21122-2-211-1-1-1-111110000000000002211-1-111-1-100000000
χ29222-2-22-2-222-2-222-222-2-2-200002-22-2002i−2i0000000000000000000022-2-200000000002i−2i0000002i−2i00
χ30222-2-22-2-222-2-222-222-2-2-200002-22-2002i−2i00000000000000000000-2-22200000000002i−2i000000−2i2i00
χ31222-2-22-2-222-2-222-222-2-2-200002-22-200−2i2i0000000000000000000022-2-20000000000−2i2i000000−2i2i00
χ32222-2-22-2-222-2-222-222-2-2-200002-22-200−2i2i00000000000000000000-2-2220000000000−2i2i0000002i−2i00
χ332-2-22-22-2222-22-2-222-22-2-200002-2-222i−2i00000000000000000000002i−2i2i−2i0000002i−2i000000002-20000
χ342-2-22-22-2222-22-2-222-22-2-200002-2-222i−2i0000000000000000000000−2i2i−2i2i0000002i−2i00000000-220000
χ352-2-22-22-2222-22-2-222-22-2-200002-2-22−2i2i00000000000000000000002i−2i2i−2i000000−2i2i00000000-220000
χ362-2-22-22-2222-22-2-222-22-2-200002-2-22−2i2i0000000000000000000000−2i2i−2i2i000000−2i2i000000002-20000
χ372-2-2-2222-2222-2-2-2-22-2-222000022-2-20000002i−2i00002i2i−2i−2i00002-22-22i−2i−2i2i0000000000000000000000
χ382-2-2-2222-2222-2-2-2-22-2-222000022-2-20000002i−2i00002i2i−2i−2i0000-22-22−2i2i2i−2i0000000000000000000000
χ392-2-2-2222-2222-2-2-2-22-2-222000022-2-2000000−2i2i0000−2i−2i2i2i00002-22-2−2i2i2i−2i0000000000000000000000
χ402-2-2-2222-2222-2-2-2-22-2-222000022-2-2000000−2i2i0000−2i−2i2i2i0000-22-222i−2i−2i2i0000000000000000000000
χ412-2-2-2222-22-2-222-2-22-2-2220000-2-222000000002-200000022-2-22-2-22000022-2-2000000000000000000
χ422-2-2-2222-22-2-222-2-22-2-2220000-2-222000000002-200000022-2-2-222-20000-2-222000000000000000000
χ432-2-2-2222-22-2-222-2-22-2-2220000-2-22200000000-22000000-2-2222-2-220000-2-222000000000000000000
χ442-2-2-2222-22-2-222-2-22-2-2220000-2-22200000000-22000000-2-222-222-2000022-2-2000000000000000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-244-4-422220000-2-200002200000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422220000220000-2-200000000000000000000000000000000000000
χ47444-4-44-4-44-444-44-444-4-4-40000-44-4400000000000000000000000000000000000000000000000000
χ48444-4-44-4-4-24-4-44-22-2-22220000-22-22004i−4i0000000000000000000000000000000000−2i2i0000000000
χ49444-4-44-4-4-24-4-44-22-2-22220000-22-2200−4i4i00000000000000000000000000000000002i−2i0000000000
χ50444-4-44-4-4-2-444-4-22-2-222200002-22-2000000000000000000000000000000000000000023−2300000000
χ51444-4-44-4-4-2-444-4-22-2-222200002-22-20000000000000000000000000000000000000000−232300000000
χ5244-444-4-4-4400004-4-4-444-44-400000000004-400000000000000000000000000000000000000000000
χ5344-444-4-4-4400004-4-4-444-4-440000000000-4400000000000000000000000000000000000000000000
χ5444-444-4-4-4-20000-2222-2-224-40000000000-220000006−66−66−66−6000000000000000000000000000000
χ5544-444-4-4-4-20000-2222-2-224-40000000000-22000000−66−66−66−66000000000000000000000000000000
χ5644-444-4-4-4-20000-2222-2-22-4400000000002-20000006−66−6−66−66000000000000000000000000000000
χ5744-444-4-4-4-20000-2222-2-22-4400000000002-2000000−66−666−66−6000000000000000000000000000000
χ5844-4-4-4-4444000044-4-4-4-44000000000000000000000000000000000000−2i22i2−2i22i2000000000000000000
χ5944-4-4-4-4444000044-4-4-4-440000000000000000000000000000000000002i2−2i22i2−2i2000000000000000000
χ604-444-4-44-440000-4-4-444-44000000000000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ614-444-4-44-440000-4-4-444-440000000000000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ624-44-44-4-4440000-44-44-44-4004i−4i000000000000004i−4i00000000000000000000000000000000000000
χ634-44-44-4-4440000-44-44-44-400−4i4i00000000000000−4i4i00000000000000000000000000000000000000
χ644-44-44-4-44-200002-22-22-22004i−4i00000000000000−2i2ii6−i6−i6i66−6−66000000000000000000000000000000
χ654-44-44-4-44-200002-22-22-22004i−4i00000000000000−2i2i−i6i6i6−i6−666−6000000000000000000000000000000
χ664-44-44-4-44-200002-22-22-2200−4i4i000000000000002i−2ii6−i6−i6i6−666−6000000000000000000000000000000
χ674-44-44-4-44-200002-22-22-2200−4i4i000000000000002i−2i−i6i6i6−i66−6−66000000000000000000000000000000
χ684-4-44-44-444-44-44-444-44-4-40000-444-400000000000000000000000000000000000000000000000000
χ694-4-44-44-44-24-44-42-2-22-2220000-222-24i−4i00000000000000000000000000000000−2i2i00000000000000
χ704-4-44-44-44-24-44-42-2-22-2220000-222-2−4i4i000000000000000000000000000000002i−2i00000000000000
χ714-4-44-44-44-2-44-442-2-22-22200002-2-2200000000000000000000000000000000000023−23000000000000
χ724-4-44-44-44-2-44-442-2-22-22200002-2-22000000000000000000000000000000000000−2323000000000000
χ734-4-4-4444-4-244-4-422-222-2-20000-2-2220000004i−4i0000−2i−2i2i2i0000000000000000000000000000000000
χ744-4-4-4444-4-244-4-422-222-2-20000-2-222000000−4i4i00002i2i−2i−2i0000000000000000000000000000000000
χ754-4-4-4444-4-2-4-44422-222-2-2000022-2-2000000004-4000000-2-222000000000000000000000000000000
χ764-4-4-4444-4-2-4-44422-222-2-2000022-2-200000000-4400000022-2-2000000000000000000000000000000
χ7788-8-8-8-888-40000-4-44444-40000000000000000000000000000000000000000000000000000000000
χ788-888-8-88-8-40000444-4-44-40000000000000000000000000000000000000000000000000000000000

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