Finite Group Databasebeta

← Group #10896436

Character table — Group #10896436

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222244448888888888888888888888888812121212121212121616161616161616242424242424242424242424
order1222222234444666666612121212224444444488881212121224242424242424244444444466121212121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111
χ511111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111
χ811111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1
χ9111111111111111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-1-1-1
χ10111111111111111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111
χ11111111111111111111111111-1-111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ12111111111111111111111111-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ13111111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111
χ14111111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-111-1-111-1-1
χ15111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1
χ16111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-111
χ17222222222-2-2-2-22222222-2-2-2-2002-2000000000022-2-20000000022-2-222-2-200000000000000000000
χ18222222222-2-2-2-22222222-2-2-2-2002-2000000000022-2-200000000-2-222-2-22200000000000000000000
χ19222222222-2-2-2-22222222-2-2-2-200-220000000000-2-2220000000022-2-2-2-22200000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-200-220000000000-2-22200000000-2-22222-2-200000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-222-2-2-2-2-1-1-1-11111111100000000-1-1-1-11111000000000000
χ2322222222-12222-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-222-2-21111-1-1-1-1111100000000-1-111-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-22211111111-1-1-1-100000000-1-11111-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-2222222-2-2-2-2-2-2-1-1-1-111111111000000001111-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000000011111111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-222-2-22211111111-1-1-1-10000000011-1-1-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2222222-2-21111-1-1-1-111110000000011-1-111-1-1000000000000
χ292222-2-2-2-2222-2-2222-2-2-2-222-2-22-20000000000000000000000002-22-200002-20000002-20000000000
χ302222-2-2-2-2222-2-2222-2-2-2-222-2-22-2000000000000000000000000-22-2200002-2000000-220000000000
χ312222-2-2-2-2222-2-2222-2-2-2-222-2-2-220000000000000000000000002-22-20000-22000000-220000000000
χ322222-2-2-2-2222-2-2222-2-2-2-222-2-2-22000000000000000000000000-22-220000-220000002-20000000000
χ332222-2-2-2-22-2-222222-2-2-2-2-2-222000000002i−2i00000000000000002-2-220000002i−2i00000000002i−2i0000
χ342222-2-2-2-22-2-222222-2-2-2-2-2-222000000002i−2i0000000000000000-222-20000002i−2i0000000000−2i2i0000
χ352222-2-2-2-22-2-222222-2-2-2-2-2-22200000000−2i2i00000000000000002-2-22000000−2i2i0000000000−2i2i0000
χ362222-2-2-2-22-2-222222-2-2-2-2-2-22200000000−2i2i0000000000000000-222-2000000−2i2i00000000002i−2i0000
χ372-2-2222-2-222-22-2-2-2222-2-22-22-20000002i−2i00000000000000000000002i−2i2i−2i0000002i−2i002-200000000
χ382-2-2222-2-222-22-2-2-2222-2-22-22-20000002i−2i0000000000000000000000−2i2i−2i2i0000002i−2i00-2200000000
χ392-2-2222-2-222-22-2-2-2222-2-22-22-2000000−2i2i00000000000000000000002i−2i2i−2i000000−2i2i00-2200000000
χ402-2-2222-2-222-22-2-2-2222-2-22-22-2000000−2i2i0000000000000000000000−2i2i−2i2i000000−2i2i002-200000000
χ412-2-2222-2-22-22-22-2-2222-2-2-22-2200002i−2i0000000000000000000000002i−2i−2i2i00002i−2i0000002-2000000
χ422-2-2222-2-22-22-22-2-2222-2-2-22-2200002i−2i000000000000000000000000−2i2i2i−2i00002i−2i000000-22000000
χ432-2-2222-2-22-22-22-2-2222-2-2-22-220000−2i2i0000000000000000000000002i−2i−2i2i0000−2i2i000000-22000000
χ442-2-2222-2-22-22-22-2-2222-2-2-22-220000−2i2i000000000000000000000000−2i2i2i−2i0000−2i2i0000002-2000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-22222004-40000000000-2-222000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2222200-44000000000022-2-2000000000000000000000000000000000000
χ474444-4-4-4-4-244-4-4-2-2-22222-2-2224-400000000000000000000000000000000-22000000000000000000
χ484444-4-4-4-4-244-4-4-2-2-22222-2-222-44000000000000000000000000000000002-2000000000000000000
χ494444-4-4-4-4-2-4-444-2-2-2222222-2-2000000004i−4i00000000000000000000000000−2i2i0000000000000000
χ504444-4-4-4-4-2-4-444-2-2-2222222-2-200000000−4i4i000000000000000000000000002i−2i0000000000000000
χ5144-4-44-44-4400004-4-44-4-4400000000000000000000000000000000000000000000000000000000−2i22i2
χ5244-4-44-44-4400004-4-44-4-44000000000000000000000000000000000000000000000000000000002i2−2i2
χ5344-4-4-44-44400004-4-4-444-40000000000000000−2i22i200000000−2i2−2i22i22i20000000000000000000000000000
χ5444-4-4-44-44400004-4-4-444-400000000000000002i2−2i2000000002i22i2−2i2−2i20000000000000000000000000000
χ5544-4-4-44-44-20000-2222-2-220000000000000000−2i22i200−2i32i366−6−6i2i2−i2−i20000000000000000000000000000
χ5644-4-4-44-44-20000-2222-2-220000000000000000−2i22i2002i3−2i3−6−666i2i2−i2−i20000000000000000000000000000
χ5744-4-4-44-44-20000-2222-2-2200000000000000002i2−2i200−2i32i3−6−666−i2−i2i2i20000000000000000000000000000
χ5844-4-4-44-44-20000-2222-2-2200000000000000002i2−2i2002i3−2i366−6−6−i2−i2i2i20000000000000000000000000000
χ594-44-44-4-4440000-44-44-44-400000000000000−2i22i2000000−2i22i2−2i22i200000000000000000000000000000000
χ604-44-44-4-4440000-44-44-44-4000000000000002i2−2i20000002i2−2i22i2−2i200000000000000000000000000000000
χ614-44-44-4-44-200002-22-22-2200000000000000−2i22i200−2i32i300i2−i2i2−i26−66−60000000000000000000000000000
χ624-44-44-4-44-200002-22-22-2200000000000000−2i22i2002i3−2i300i2−i2i2−i2−66−660000000000000000000000000000
χ634-44-44-4-44-200002-22-22-22000000000000002i2−2i200−2i32i300−i2i2−i2i2−66−660000000000000000000000000000
χ644-44-44-4-44-200002-22-22-22000000000000002i2−2i2002i3−2i300−i2i2−i2i26−66−60000000000000000000000000000
χ654-44-4-444-440000-44-4-44-44000000000000000000000000000000000000000000000000000000−2i22i200
χ664-44-4-444-440000-44-4-44-440000000000000000000000000000000000000000000000000000002i2−2i200
χ674-4-4444-4-4-24-44-422-2-2-222-22-220000004i−4i00000000000000000000000000000000−2i2i000000000000
χ684-4-4444-4-4-24-44-422-2-2-222-22-22000000−4i4i000000000000000000000000000000002i−2i000000000000
χ694-4-4444-4-4-2-44-4422-2-2-2222-22-200004i−4i00000000000000000000000000000000−2i2i00000000000000
χ704-4-4444-4-4-2-44-4422-2-2-2222-22-20000−4i4i000000000000000000000000000000002i−2i00000000000000
χ714-4-44-4-44444-4-44-4-44-4-4444-4-44000000000000000000000000000000000000000000000000000000
χ724-4-44-4-4444-444-4-4-44-4-444-444-4000000000000000000000000000000000000000000000000000000
χ734-4-44-4-444-24-4-4422-222-2-2-222-20000000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ744-4-44-4-444-24-4-4422-222-2-2-222-200000000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ754-4-44-4-444-2-444-422-222-2-22-2-22000000000000000000−2i32i32i3−2i300000000000000000000000000000000
χ764-4-44-4-444-2-444-422-222-2-22-2-220000000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ7788-8-88-88-8-40000-444-444-40000000000000000000000000000000000000000000000000000000000
χ788-88-8-888-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000

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