Finite Group Databasebeta

← Group #10828540

Character table — Group #10828540

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222244448888888888888888888888888812121212121212121616161616161616242424242424242424242424
order12222222344446666666121212122222444444888812121212242424242424242422444444666612121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111
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
χ711111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ811111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-111-1-111-1-1
χ9111111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-111-1-1-1-111
χ10111111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-1
χ11111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1
χ12111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-111
χ13111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-1-1
χ14111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111
χ15111111111111111111111111-1-1-1-1-1-111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ16111111111111111111111111-1-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ17222222222-2-2-2-22222222-2-2-2-20000002-200000022-2-20000000022-2-2-2-22200000000000000000000
χ18222222222-2-2-2-22222222-2-2-2-20000002-200000022-2-200000000-2-22222-2-200000000000000000000
χ19222222222-2-2-2-22222222-2-2-2-2000000-22000000-2-2220000000022-2-222-2-200000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-2000000-22000000-2-22200000000-2-222-2-22200000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-1-1-1-1-12222-2-222-2-2-2-2-2-2-1-1-1-11111111100000000-1-1-1-11111000000000000
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
χ2422222222-12222-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-222-2-22211111111-1-1-1-100000000-1-11111-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-22211111111-1-1-1-10000000011-1-1-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-22222-2-21111-1-1-1-111110000000011-1-111-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222222-2-2-2-2-1-1-1-111111111000000001111-1-1-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000000011111111000000000000
χ292-2-2222-2-2222-2-22-2-22-22-2-2-22200002-20000000000000000000000002i−2i2i−2i00002-2000000002i−2i0000
χ302-2-2222-2-2222-2-22-2-22-22-2-2-22200002-2000000000000000000000000−2i2i−2i2i00002-200000000−2i2i0000
χ312-2-2222-2-2222-2-22-2-22-22-2-2-2220000-220000000000000000000000002i−2i2i−2i0000-2200000000−2i2i0000
χ322-2-2222-2-2222-2-22-2-22-22-2-2-2220000-22000000000000000000000000−2i2i−2i2i0000-22000000002i−2i0000
χ332-2-2222-2-22-2-2222-2-22-22-222-2-2000000002i−2i000000000000000000002i−2i−2i2i0000002i−2i2-20000000000
χ342-2-2222-2-22-2-2222-2-22-22-222-2-2000000002i−2i00000000000000000000−2i2i2i−2i0000002i−2i-220000000000
χ352-2-2222-2-22-2-2222-2-22-22-222-2-200000000−2i2i000000000000000000002i−2i−2i2i000000−2i2i-220000000000
χ362-2-2222-2-22-2-2222-2-22-22-222-2-200000000−2i2i00000000000000000000−2i2i2i−2i000000−2i2i2-20000000000
χ372-2-2-22-22222-22-2-2-2-222-222-22-2002-200000000000000000000002-22-20000002-2000000002-2000000
χ382-2-2-22-22222-22-2-2-2-222-222-22-2002-20000000000000000000000-22-220000002-200000000-22000000
χ392-2-2-22-22222-22-2-2-2-222-222-22-200-2200000000000000000000002-22-2000000-2200000000-22000000
χ402-2-2-22-22222-22-2-2-2-222-222-22-200-220000000000000000000000-22-22000000-22000000002-2000000
χ412-2-2-22-2222-22-22-2-2-222-22-22-222-20000000000000000000000002-2-2200002-2000000002-200000000
χ422-2-2-22-2222-22-22-2-2-222-22-22-222-2000000000000000000000000-222-200002-200000000-2200000000
χ432-2-2-22-2222-22-22-2-2-222-22-22-22-220000000000000000000000002-2-220000-2200000000-2200000000
χ442-2-2-22-2222-22-22-2-2-222-22-22-22-22000000000000000000000000-222-20000-22000000002-200000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-222220000004-4000000-2-222000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-22222000000-4400000022-2-2000000000000000000000000000000000000
χ47444-44-4-4-444-4-44-4444-4-4-4-444-4000000000000000000000000000000000000000000000000000000
χ48444-44-4-4-44-444-4-4444-4-4-44-4-44000000000000000000000000000000000000000000000000000000
χ49444-44-4-4-4-24-4-442-2-2-22222-2-2200000000000000000000002323−23−230000000000000000000000000000
χ50444-44-4-4-4-24-4-442-2-2-22222-2-220000000000000000000000−23−2323230000000000000000000000000000
χ51444-44-4-4-4-2-444-42-2-2-2222-222-20000000000000000002323−23−2300000000000000000000000000000000
χ52444-44-4-4-4-2-444-42-2-2-2222-222-2000000000000000000−23−23232300000000000000000000000000000000
χ5344-44-4-44-440000-44-4-444-400000000000000000000000000000000000000000000000000000000−2i22i2
χ5444-44-4-44-440000-44-4-444-4000000000000000000000000000000000000000000000000000000002i2−2i2
χ5544-4-4-44-444000044-4-4-4-4400000000000000000000000000000000000000000000000000000022−2200
χ5644-4-4-44-444000044-4-4-4-44000000000000000000000000000000000000000000000000000000−222200
χ574-444-4-4-4440000-4-44-4-4440000000000000022−2200000022−2222−2200000000000000000000000000000000
χ584-444-4-4-4440000-4-44-4-44400000000000000−2222000000−2222−222200000000000000000000000000000000
χ594-444-4-4-44-2000022-222-2-20000000000000022−220000−2i32i3−22−22i6−i6i6−i60000000000000000000000000000
χ604-444-4-4-44-2000022-222-2-20000000000000022−2200002i3−2i3−22−22−i6i6−i6i60000000000000000000000000000
χ614-444-4-4-44-2000022-222-2-200000000000000−22220000−2i32i32−22−2−i6i6−i6i60000000000000000000000000000
χ624-444-4-4-44-2000022-222-2-200000000000000−222200002i3−2i32−22−2i6−i6i6−i60000000000000000000000000000
χ634-44-4-444-4400004-44-44-4-40000000000000000−2i22i200000000−2i22i22i2−2i20000000000000000000000000000
χ644-44-4-444-4400004-44-44-4-400000000000000002i2−2i2000000002i2−2i2−2i22i20000000000000000000000000000
χ654-44-4-444-4-20000-22-22-2220000000000000000−2i22i2−2i32i3006−6−66i2−i2−i2i20000000000000000000000000000
χ664-44-4-444-4-20000-22-22-2220000000000000000−2i22i22i3−2i300−666−6i2−i2−i2i20000000000000000000000000000
χ674-44-4-444-4-20000-22-22-22200000000000000002i2−2i2−2i32i300−666−6−i2i2i2−i20000000000000000000000000000
χ684-44-4-444-4-20000-22-22-22200000000000000002i2−2i22i3−2i3006−6−66−i2i2i2−i20000000000000000000000000000
χ694-4-4444-4-4-244-4-4-222-22-2222-2-200004-400000000000000000000000000000000-2200000000000000
χ704-4-4444-4-4-244-4-4-222-22-2222-2-20000-44000000000000000000000000000000002-200000000000000
χ714-4-4444-4-4-2-4-444-222-22-22-2-222000000004i−4i000000000000000000000000000000−2i2i000000000000
χ724-4-4444-4-4-2-4-444-222-22-22-2-22200000000−4i4i0000000000000000000000000000002i−2i000000000000
χ734-4-4-44-444-24-44-4222-2-22-2-22-22004-400000000000000000000000000000000-220000000000000000
χ744-4-4-44-444-24-44-4222-2-22-2-22-2200-44000000000000000000000000000000002-20000000000000000
χ754-4-4-44-444-2-44-44222-2-22-22-22-24-400000000000000000000000000000000-22000000000000000000
χ764-4-4-44-444-2-44-44222-2-22-22-22-2-44000000000000000000000000000000002-2000000000000000000
χ7788-88-8-88-8-400004-444-4-440000000000000000000000000000000000000000000000000000000000
χ7888-8-8-88-88-40000-4-44444-40000000000000000000000000000000000000000000000000000000000

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