Finite Group Databasebeta

← Group #10826081

Character table — Group #10826081

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order124422234446668888888812121212661212242424242424242424444466888888121212121212121212122424242424242424242424242444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ511111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ611111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ711111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ911111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1
χ1011111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111
χ1111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ1211111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ1311111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-1-1
χ1411111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-11111
χ1511111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111
χ1611111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1
χ172222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-122-2-2-2-21111-1-111111111-1-1-1-111110000000000000000
χ192222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-211-2-222-2-2-1-1-1-1111111-1-1-1-1111111110000000000000000
χ202222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211-2-2-2-222111111-1-1-1-111111111-1-1-1-10000000000000000
χ212222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111112222-2-2-1-1-2-2-2-222-1-1-1-1-1-1111111111111-1-1-1-10000000000000000
χ222222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-222-1-1-2-222-2-21111-1-1-1-1-1-1-1-1-1-1111111110000000000000000
χ232222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-222221122-2-2-2-2-1-1-1-111-1-1-1-11111-1-1-1-111110000000000000000
χ242222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-2-2-2-2-2112222221111111111-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2522222-2-222-2-22222222-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000002i−2i0000002i−2i0000
χ2622222-2-222-2-22222222-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000000000−2i2i000000−2i2i0000
χ2722222-2-222-2-2222-2-2-2-222222222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000002i−2i000000−2i2i0000
χ2822222-2-222-2-2222-2-2-2-222222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000−2i2i0000002i−2i0000
χ292222-22-22-22-2-2-2222-2-222-2-2-2-2222-22-222-2-222-2-2002i−2i0000002i−2i002i2i−2i−2i0000002i2i−2i−2i000000000000000000000000
χ302222-22-22-22-2-2-2222-2-222-2-2-2-2222-22-222-2-222-2-200−2i2i000000−2i2i00−2i−2i2i2i000000−2i−2i2i2i000000000000000000000000
χ312222-22-22-22-2-2-22-2-222-2-222-2-2222-22-2-2-222-2-222002i−2i000000−2i2i002i2i−2i−2i000000−2i−2i2i2i000000000000000000000000
χ322222-22-22-22-2-2-22-2-222-2-222-2-2222-22-2-2-222-2-22200−2i2i0000002i−2i00−2i−2i2i2i0000002i2i−2i−2i000000000000000000000000
χ332222-22-2-1-22-211-122-2-222-2-211-1-1-11-11-1-111-1-111002i−2i00−i3i3002i−2i00−i−iii−i3i333−3−3−i−iii−i3−i3i3i333−3−30000000000000000
χ342222-22-2-1-22-211-122-2-222-2-211-1-1-11-11-1-111-1-111002i−2i00i3−i3002i−2i00−i−iiii3−i3−3−333−i−iiii3i3−i3−i3−3−3330000000000000000
χ352222-22-2-1-22-211-122-2-222-2-211-1-1-11-11-1-111-1-11100−2i2i00−i3i300−2i2i00ii−i−i−i3i3−3−333ii−i−i−i3−i3i3i3−3−3330000000000000000
χ362222-22-2-1-22-211-122-2-222-2-211-1-1-11-11-1-111-1-11100−2i2i00i3−i300−2i2i00ii−i−ii3−i333−3−3ii−i−ii3i3−i3−i333−3−30000000000000000
χ372222-22-2-1-22-211-1-2-222-2-22211-1-1-11-1111-1-111-1-1002i−2i00−i3i300−2i2i00−i−iii−i3i3−3−333ii−i−ii3i3−i3−i333−3−30000000000000000
χ382222-22-2-1-22-211-1-2-222-2-22211-1-1-11-1111-1-111-1-1002i−2i00i3−i300−2i2i00−i−iiii3−i333−3−3ii−i−i−i3−i3i3i3−3−3330000000000000000
χ392222-22-2-1-22-211-1-2-222-2-22211-1-1-11-1111-1-111-1-100−2i2i00−i3i3002i−2i00ii−i−i−i3i333−3−3−i−iiii3i3−i3−i3−3−3330000000000000000
χ402222-22-2-1-22-211-1-2-222-2-22211-1-1-11-1111-1-111-1-100−2i2i00i3−i3002i−2i00ii−i−ii3−i3−3−333−i−iii−i3−i3i3i333−3−30000000000000000
χ412222-2-222-2-22-2-2222-2-2-2-222-2-222-22-2222-2-2-2-22200000000000000000000000000000000000000002-20000002-200
χ422222-2-222-2-22-2-2222-2-2-2-222-2-222-22-2222-2-2-2-2220000000000000000000000000000000000000000-22000000-2200
χ432222-2-222-2-22-2-22-2-22222-2-2-2-222-22-22-2-22222-2-200000000000000000000000000000000000000002-2000000-2200
χ442222-2-222-2-22-2-22-2-22222-2-2-2-222-22-22-2-22222-2-20000000000000000000000000000000000000000-220000002-200
χ4522-2-22222-2-2-22222i−2i2i−2i2i−2i2i−2i-2-2-2-222-2-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000002-20000002i−2i
χ4622-2-22222-2-2-22222i−2i2i−2i2i−2i2i−2i-2-2-2-222-2-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000-22000000−2i2i
χ4722-2-22222-2-2-2222−2i2i−2i2i−2i2i−2i2i-2-2-2-222-2-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000002-2000000−2i2i
χ4822-2-22222-2-2-2222−2i2i−2i2i−2i2i−2i2i-2-2-2-222-2-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000-220000002i−2i
χ4922-2-22-2-22-2222222i−2i2i−2i−2i2i−2i2i-2-2-2-2-2-2222i−2i2i−2i−2i2i−2i2i2-20000222i−2i00000000-2-2000000002i−2i2i−2i00000000000000000000
χ5022-2-22-2-22-2222222i−2i2i−2i−2i2i−2i2i-2-2-2-2-2-2222i−2i2i−2i−2i2i−2i2i-220000-2-2−2i2i000000002200000000−2i2i−2i2i00000000000000000000
χ5122-2-22-2-22-222222−2i2i−2i2i2i−2i2i−2i-2-2-2-2-2-222−2i2i−2i2i2i−2i2i−2i2-2000022−2i2i00000000-2-200000000−2i2i−2i2i00000000000000000000
χ5222-2-22-2-22-222222−2i2i−2i2i2i−2i2i−2i-2-2-2-2-2-222−2i2i−2i2i2i−2i2i−2i-220000-2-22i−2i0000000022000000002i−2i2i−2i00000000000000000000
χ5322-2-22-2-2-1-222-1-1-12i−2i2i−2i−2i2i−2i2i111111-1-1−ii−iii−ii−i2-20000-1-12i−2i0000−i3i3−i3i3113−33−33−33−3−ii−ii−i3i3−i3i30000000000000000
χ5422-2-22-2-2-1-222-1-1-12i−2i2i−2i−2i2i−2i2i111111-1-1−ii−iii−ii−i2-20000-1-12i−2i0000i3−i3i3−i311−33−33−33−33−ii−iii3−i3i3−i30000000000000000
χ5522-2-22-2-2-1-222-1-1-12i−2i2i−2i−2i2i−2i2i111111-1-1−ii−iii−ii−i-22000011−2i2i0000−i3i3−i3i3-1-1−33−333−33−3i−ii−ii3−i3i3−i30000000000000000
χ5622-2-22-2-2-1-222-1-1-12i−2i2i−2i−2i2i−2i2i111111-1-1−ii−iii−ii−i-22000011−2i2i0000i3−i3i3−i3-1-13−33−3−33−33i−ii−i−i3i3−i3i30000000000000000
χ5722-2-22-2-2-1-222-1-1-1−2i2i−2i2i2i−2i2i−2i111111-1-1i−ii−i−ii−ii2-20000-1-1−2i2i0000−i3i3−i3i311−33−33−33−33i−ii−i−i3i3−i3i30000000000000000
χ5822-2-22-2-2-1-222-1-1-1−2i2i−2i2i2i−2i2i−2i111111-1-1i−ii−i−ii−ii2-20000-1-1−2i2i0000i3−i3i3−i3113−33−33−33−3i−ii−ii3−i3i3−i30000000000000000
χ5922-2-22-2-2-1-222-1-1-1−2i2i−2i2i2i−2i2i−2i111111-1-1i−ii−i−ii−ii-220000112i−2i0000−i3i3−i3i3-1-13−33−3−33−33−ii−iii3−i3i3−i30000000000000000
χ6022-2-22-2-2-1-222-1-1-1−2i2i−2i2i2i−2i2i−2i111111-1-1i−ii−i−ii−ii-220000112i−2i0000i3−i3i3−i3-1-1−33−333−33−3−ii−ii−i3i3−i3i30000000000000000
χ6122-2-2-22-222-22-2-222i−2i−2i2i2i−2i−2i2i22-2-22-2-222i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000002-20000002i−2i000000
χ6222-2-2-22-222-22-2-222i−2i−2i2i2i−2i−2i2i22-2-22-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000-22000000−2i2i000000
χ6322-2-2-22-222-22-2-22−2i2i2i−2i−2i2i2i−2i22-2-22-2-22−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000002-2000000−2i2i000000
χ6422-2-2-22-222-22-2-22−2i2i2i−2i−2i2i2i−2i22-2-22-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000-220000002i−2i000000
χ6522-2-2-2-22222-2-2-222i−2i−2i2i−2i2i2i−2i22-2-2-222-22i−2i−2i2i−2i2i2i−2i00002-20000002i−2i0000002-2-2200000000−2i2i2i−2i0000000000000000
χ6622-2-2-2-22222-2-2-222i−2i−2i2i−2i2i2i−2i22-2-2-222-22i−2i−2i2i−2i2i2i−2i0000-22000000−2i2i000000-222-2000000002i−2i−2i2i0000000000000000
χ6722-2-2-2-22222-2-2-22−2i2i2i−2i2i−2i−2i2i22-2-2-222-2−2i2i2i−2i2i−2i−2i2i00002-2000000−2i2i0000002-2-22000000002i−2i−2i2i0000000000000000
χ6822-2-2-2-22222-2-2-22−2i2i2i−2i2i−2i−2i2i22-2-2-222-2−2i2i2i−2i2i−2i−2i2i0000-220000002i−2i000000-222-200000000−2i2i2i−2i0000000000000000
χ6922-2-2-2-22-122-211-12i−2i−2i2i−2i2i2i−2i-1-1111-1-11−iii−ii−i−ii00002-2−i3i300002i−2i−333−3i3−i3-111-1−i3i3i3−i33−3−33i−i−ii0000000000000000
χ7022-2-2-2-22-122-211-12i−2i−2i2i−2i2i2i−2i-1-1111-1-11−iii−ii−i−ii00002-2i3−i300002i−2i3−3−33−i3i3-111-1i3−i3−i3i3−333−3i−i−ii0000000000000000
χ7122-2-2-2-22-122-211-12i−2i−2i2i−2i2i2i−2i-1-1111-1-11−iii−ii−i−ii0000-22−i3i30000−2i2i3−3−33i3−i31-1-11i3−i3−i3i33−3−33−iii−i0000000000000000
χ7222-2-2-2-22-122-211-12i−2i−2i2i−2i2i2i−2i-1-1111-1-11−iii−ii−i−ii0000-22i3−i30000−2i2i−333−3−i3i31-1-11−i3i3i3−i3−333−3−iii−i0000000000000000
χ7322-2-2-2-22-122-211-1−2i2i2i−2i2i−2i−2i2i-1-1111-1-11i−i−ii−iii−i00002-2−i3i30000−2i2i3−3−33i3−i3-111-1−i3i3i3−i3−333−3−iii−i0000000000000000
χ7422-2-2-2-22-122-211-1−2i2i2i−2i2i−2i−2i2i-1-1111-1-11i−i−ii−iii−i00002-2i3−i30000−2i2i−333−3−i3i3-111-1i3−i3−i3i33−3−33−iii−i0000000000000000
χ7522-2-2-2-22-122-211-1−2i2i2i−2i2i−2i−2i2i-1-1111-1-11i−i−ii−iii−i0000-22−i3i300002i−2i−333−3i3−i31-1-11i3−i3−i3i3−333−3i−i−ii0000000000000000
χ7622-2-2-2-22-122-211-1−2i2i2i−2i2i−2i−2i2i-1-1111-1-11i−i−ii−iii−i0000-22i3−i300002i−2i3−3−33−i3i31-1-11−i3i3i3−i33−3−33i−i−ii0000000000000000
χ7744444-4-4-24-4-4-2-2-24444-4-4-4-4-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000000000000000
χ7844444-4-4-24-4-4-2-2-2-4-4-4-44444-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000000000000000
χ794444-4-44-2-4-4422-244-4-4-4-44422-2-22-22-2-2-22222-2-20000000000000000000000000000000000000000000000000000
χ804444-4-44-2-4-4422-2-4-44444-4-422-2-22-22-222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ8144-4-4444-2-4-4-4-2-2-24i−4i4i−4i4i−4i4i−4i2222-2-222−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ8244-4-4444-2-4-4-4-2-2-2−4i4i−4i4i−4i4i−4i4i2222-2-2222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ8344-4-4-44-4-24-4422-24i−4i−4i4i4i−4i−4i4i-2-222-222-2−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ8444-4-4-44-4-24-4422-2−4i4i4i−4i−4i4i4i−4i-2-222-222-22i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ858-88i−8i000800000-800000000008i−8i0000000000000000000000000000000000000000000000000000000000000000
χ868-88i−8i000-4000−4i34i340000000043−43−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ878-88i−8i000-40004i3−4i3400000000−4343−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ888-8−8i8i000800000-80000000000−8i8i0000000000000000000000000000000000000000000000000000000000000000
χ898-8−8i8i000-4000−4i34i3400000000−43434i−4i0000000000000000000000000000000000000000000000000000000000000000
χ908-8−8i8i000-40004i3−4i340000000043−434i−4i0000000000000000000000000000000000000000000000000000000000000000

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