Finite Group Databasebeta

← Group #10696625

Character table — Group #10696625

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size111122222222444444444448888161616161616161616161616161616161616242424242424242448484848
order122222344666444446612121212121212122444668812121212121224242424444488884488
χ1111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-11-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111111111111-11-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-111
χ6111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1
χ7111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1
χ8111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ9222222222222-2-22-2-222-2-222-2-2-2220-20220000-2-2000000000000000000
χ10222222222222-2-22-2-222-2-222-2-2-22-2020-2-2000022000000000000000000
χ112222222-2-22222-2-22-22222-2-22-2-2-2000000000000000000000000002-200
χ122222222-2-22222-2-22-22222-2-22-2-2-200000000000000000000000000-2200
χ132222222-2-2222-22-2-2222-2-2-2-2-222-200000000000000000022-2-200000000
χ142222222-2-2222-22-2-2222-2-2-2-2-222-2000000000000000000-2-22200000000
χ15222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-122-1-1-1-1-1-1-1-1-1-1000000000000
χ16222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12-22-2-1-1-2-211-1-1111111000000000000
χ17222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-22-2211-2-2-1-111-1-11111000000000000
χ18222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-21122111111-1-1-1-1000000000000
χ19222222-122-1-1-1-2-22-2-2-1-111-1-1111-120-20-1-100−i3i311−i3i3−i3−i3i3i3000000000000
χ20222222-122-1-1-1-2-22-2-2-1-111-1-1111-120-20-1-100i3−i311i3−i3i3i3−i3−i3000000000000
χ21222222-122-1-1-1-2-22-2-2-1-111-1-1111-1-20201100−i3i3-1-1−i3i3i3i3−i3−i3000000000000
χ22222222-122-1-1-1-2-22-2-2-1-111-1-1111-1-20201100i3−i3-1-1i3−i3−i3−i3i3i3000000000000
χ232222-2-22222222-2-2-22-2-22222-22-2-20000002-20000002-22-2000000000000
χ242222-2-22222222-2-2-22-2-22222-22-2-2000000-22000000-22-22000000000000
χ252222-2-2222222-22-22-2-2-2-2-2222-22-2020-200002200-2-20000000000000000
χ262222-2-2222222-22-22-2-2-2-2-2222-22-20-2020000-2-200220000000000000000
χ272222-2-22-2-2222222-2-2-2-222-2-2-2-22200000000000000000000000000002i−2i
χ282222-2-22-2-2222222-2-2-2-222-2-2-2-2220000000000000000000000000000−2i2i
χ292222-2-22-2-2222-2-2222-2-2-2-2-2-222-22000000000000000000000022-2-20000
χ302222-2-22-2-2222-2-2222-2-2-2-2-2-222-220000000000000000000000-2-2220000
χ312222-2-2-122-1-1-12-2-2-2211-1-1-1-11-1110000−i3i32-2−i3i3−i3i3i3−i3-11-11000000000000
χ322222-2-2-122-1-1-12-2-2-2211-1-1-1-11-1110000−i3i3-22i3−i3−i3i3−i3i31-11-1000000000000
χ332222-2-2-122-1-1-12-2-2-2211-1-1-1-11-1110000i3−i32-2i3−i3i3−i3−i3i3-11-11000000000000
χ342222-2-2-122-1-1-12-2-2-2211-1-1-1-11-1110000i3−i3-22−i3i3i3−i3i3−i31-11-1000000000000
χ352222-2-2-122-1-1-1-22-22-21111-1-1-11-11020-2−i3i300-1-1i3−i311−i3i3i3−i3000000000000
χ362222-2-2-122-1-1-1-22-22-21111-1-1-11-11020-2i3−i300-1-1−i3i311i3−i3−i3i3000000000000
χ372222-2-2-122-1-1-1-22-22-21111-1-1-11-110-202−i3i30011i3−i3-1-1i3−i3−i3i3000000000000
χ382222-2-2-122-1-1-1-22-22-21111-1-1-11-110-202i3−i30011−i3i3-1-1−i3i3i3−i3000000000000
χ39444444-2-4-4-2-2-24-4-44-4-2-2-2-222-2222000000000000000000000000000000
χ40444444-2-4-4-2-2-2-44-4-44-2-222222-2-22000000000000000000000000000000
χ414444-4-4-2-4-4-2-2-2444-4-422-2-22222-2-2000000000000000000000000000000
χ424444-4-4-2-4-4-2-2-2-4-4444222222-2-22-2000000000000000000000000000000
χ4344-4-44-44004-4-4000004-40000000000000000000000000000002-22-20000
χ4444-4-44-44004-4-4000004-4000000000000000000000000000000-22-220000
χ4544-4-4-444004-4-400000-440000000000000000000000000000002-2-220000
χ4644-4-4-444004-4-400000-44000000000000000000000000000000-222-20000
χ474-4-440044-4-4-440000000004-400000000000000000000002-22-200000000
χ484-4-440044-4-4-440000000004-40000000000000000000000-22-2200000000
χ494-4-44004-44-4-44000000000-4400000000000000000000002-2-2200000000
χ504-4-44004-44-4-44000000000-440000000000000000000000-222-200000000
χ5188-8-88-8-400-44400000-4400000000000000000000000000000000000000
χ5288-8-8-88-400-444000004-400000000000000000000000000000000000000
χ538-88-800800-88-8000000000000000000000000000000000000000000000
χ548-88-800-4004-44000000043−43000000000000000000000000000000000000
χ558-88-800-4004-440000000−4343000000000000000000000000000000000000
χ568-8-8800-48-844-4000000000-440000000000000000000000000000000000
χ578-8-8800-4-8844-40000000004-40000000000000000000000000000000000

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