Finite Group Databasebeta

← Group #10824471

Character table — Group #10824471

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order12222222344444444444466666661212121212121212121212122244444444446666121212121212121212121212121212121212121288888888222244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ51111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111
χ911111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1111-11-111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1111-11-111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ1111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-11-11-1-111-1-11111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111
χ1211111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-11-11-1-111-1-11111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ1311111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ1411111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ1511111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-1-1-1-1-1111111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ1611111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1
χ17222222222-2-22222-2-2-2-2-2-22222222-2-2-2-22222-2-2-2-2002-2-22000000000022-2-20000-2-2220000000000000000000000000000
χ18222222222-2-22222-2-2-2-2-2-22222222-2-2-2-22222-2-2-2-200-222-20000000000-2-222000022-2-20000000000000000000000000000
χ19222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-222220022-2-2000000000022220000-2-2-2-20000000000000000000000000000
χ20222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-2222200-2-2220000000000-2-2-2-2000022220000000000000000000000000000
χ2122222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-222-1-1-1-11111-1-1-1-111111111111100000000000000000000
χ2322222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-21111-1-1-1-11111-1-1-1-11111111100000000000000000000
χ2422222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-22222-2-21111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ2522222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-111111111222-22-222-2-2-2-2-1-1-1-1-1-1111111-1-111-1-1-1-1111100000000000000000000
χ2622222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-11111111122-22-22-2-222-2-2-1-1-1-111-1-1111111-1-11111-1-1-1-100000000000000000000
χ2722222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-111111111-2-22-22-2-2-222221111-1-111-1-1-1-1-1-1111111-1-1-1-100000000000000000000
χ2822222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-111111111-2-2-22-2222-2-222111111-1-1-1-1-1-111-1-1-1-1-1-1111100000000000000000000
χ2922222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-11111002-2-22000000−i3−i3i3i3-1-111−i3−i3i3i311-1-1−i3−i3i3i3−i3−i3i3i300000000000000000000
χ3022222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-11111002-2-22000000i3i3−i3−i3-1-111i3i3−i3−i311-1-1i3i3−i3−i3i3i3−i3−i300000000000000000000
χ3122222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-1111100-222-2000000−i3−i3i3i311-1-1−i3−i3i3i3-1-111i3i3−i3−i3i3i3−i3−i300000000000000000000
χ3222222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-1111100-222-2000000i3i3−i3−i311-1-1i3i3−i3−i3-1-111−i3−i3i3i3−i3−i3i3i300000000000000000000
χ3322222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-10022-2-2000000−i3−i3i3i3-1-1-1-1i3i3−i3−i31111−i3−i3i3i3i3i3−i3−i300000000000000000000
χ3422222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-10022-2-2000000i3i3−i3−i3-1-1-1-1−i3−i3i3i31111i3i3−i3−i3−i3−i3i3i300000000000000000000
χ3522222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-100-2-222000000−i3−i3i3i31111i3i3−i3−i3-1-1-1-1i3i3−i3−i3−i3−i3i3i300000000000000000000
χ3622222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-100-2-222000000i3i3−i3−i31111−i3−i3i3i3-1-1-1-1−i3−i3i3i3i3i3−i3−i300000000000000000000
χ37222-22-2-2-222-22i2i−2i−2i2i2i−2i−2i2-222-2-22-2-222-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000002-200002i−2i0000
χ38222-22-2-2-222-22i2i−2i−2i2i2i−2i−2i2-222-2-22-2-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000-220000−2i2i0000
χ39222-22-2-2-222-2−2i−2i2i2i−2i−2i2i2i2-222-2-22-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000002-20000−2i2i0000
χ40222-22-2-2-222-2−2i−2i2i2i−2i−2i2i2i2-222-2-22-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000-2200002i−2i0000
χ41222-22-2-2-22-222i2i−2i−2i−2i−2i2i2i-2222-2-22-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000002-22i−2i000000
χ42222-22-2-2-22-222i2i−2i−2i−2i−2i2i2i-2222-2-22-2-2-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000-22−2i2i000000
χ43222-22-2-2-22-22−2i−2i2i2i2i2i−2i−2i-2222-2-22-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000002-2−2i2i000000
χ44222-22-2-2-22-22−2i−2i2i2i2i2i−2i−2i-2222-2-22-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000-222i−2i000000
χ4522-22-22-2-222-22i−2i2i−2i2i−2i2i−2i-222-22-2-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000002-22i−2i
χ4622-22-22-2-222-22i−2i2i−2i2i−2i2i−2i-222-22-2-22-22-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000-22−2i2i
χ4722-22-22-2-222-2−2i2i−2i2i−2i2i−2i2i-222-22-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000000000002-2−2i2i
χ4822-22-22-2-222-2−2i2i−2i2i−2i2i−2i2i-222-22-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000-222i−2i
χ4922-22-22-2-22-222i−2i2i−2i−2i2i−2i2i2-22-22-2-22-2-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000022-2-22i2i−2i−2i000000000000
χ5022-22-22-2-22-222i−2i2i−2i−2i2i−2i2i2-22-22-2-22-2-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000-2-222−2i−2i2i2i000000000000
χ5122-22-22-2-22-22−2i2i−2i2i2i−2i2i−2i2-22-22-2-22-2-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000022-2-2−2i−2i2i2i000000000000
χ5222-22-22-2-22-22−2i2i−2i2i2i−2i2i−2i2-22-22-2-22-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000-2-2222i2i−2i−2i000000000000
χ5322-2-2-2-2222222-2-222-2-22-2-22-2-22-2-222-2-222-2-222-2-220000002i−2i2i−2i0000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ5422-2-2-2-2222222-2-222-2-22-2-22-2-22-2-222-2-222-2-222-2-22000000−2i2i−2i2i000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ5522-2-2-2-222222-222-2-222-2-2-22-2-22-2-222-2-22-222-2-222-20000002i−2i−2i2i0000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ5622-2-2-2-222222-222-2-222-2-2-22-2-22-2-222-2-22-222-2-222-2000000−2i2i2i−2i000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ5722-2-2-2-2222-2-22-2-22-222-2222-2-22-2-22-222-22-2-22-222-22-2000000002-22-22-200002-22-200000000000000000000000000000000
χ5822-2-2-2-2222-2-22-2-22-222-2222-2-22-2-22-222-22-2-22-222-2-2200000000-22-22-220000-22-2200000000000000000000000000000000
χ5922-2-2-2-2222-2-2-222-22-2-22222-2-22-2-22-222-2-222-22-2-222-200000000-222-22-20000-22-2200000000000000000000000000000000
χ6022-2-2-2-2222-2-2-222-22-2-22222-2-22-2-22-222-2-222-22-2-22-22000000002-2-22-2200002-22-200000000000000000000000000000000
χ6122-2-2-2-222-1222-2-222-2-22-2-2-111-111-1-111-1-111-1-111-10000002i−2i2i−2i00−i3i3i3−i33−33−3−i3i3i3−i33−33−3−ii−ii−ii−ii00000000000000000000
χ6222-2-2-2-222-1222-2-222-2-22-2-2-111-111-1-111-1-111-1-111-10000002i−2i2i−2i00i3−i3−i3i3−33−33i3−i3−i3i3−33−33−ii−ii−ii−ii00000000000000000000
χ6322-2-2-2-222-1222-2-222-2-22-2-2-111-111-1-111-1-111-1-111-1000000−2i2i−2i2i00−i3i3i3−i3−33−33−i3i3i3−i3−33−33i−ii−ii−ii−i00000000000000000000
χ6422-2-2-2-222-1222-2-222-2-22-2-2-111-111-1-111-1-111-1-111-1000000−2i2i−2i2i00i3−i3−i3i33−33−3i3−i3−i3i33−33−3i−ii−ii−ii−i00000000000000000000
χ6522-2-2-2-222-122-222-2-222-2-2-2-111-111-1-111-11-1-111-1-110000002i−2i−2i2i00−i3i3i3−i33−3−33i3−i3−i3i33−3−33−ii−iii−ii−i00000000000000000000
χ6622-2-2-2-222-122-222-2-222-2-2-2-111-111-1-111-11-1-111-1-110000002i−2i−2i2i00i3−i3−i3i3−333−3−i3i3i3−i3−333−3−ii−iii−ii−i00000000000000000000
χ6722-2-2-2-222-122-222-2-222-2-2-2-111-111-1-111-11-1-111-1-11000000−2i2i2i−2i00−i3i3i3−i3−333−3i3−i3−i3i3−333−3i−ii−i−ii−ii00000000000000000000
χ6822-2-2-2-222-122-222-2-222-2-2-2-111-111-1-111-11-1-111-1-11000000−2i2i2i−2i00i3−i3−i3i33−3−33−i3i3i3−i33−3−33i−ii−i−ii−ii00000000000000000000
χ6922-2-2-2-222-1-2-22-2-22-222-222-111-111-11-1-11-111-11-1-112-2000000002-2-11-113−3−33-11-11−333−33−3−333−3−3300000000000000000000
χ7022-2-2-2-222-1-2-22-2-22-222-222-111-111-11-1-11-111-11-1-112-2000000002-2-11-11−333−3-11-113−3−33−333−3−333−300000000000000000000
χ7122-2-2-2-222-1-2-22-2-22-222-222-111-111-11-1-11-111-11-1-11-2200000000-221-11-13−3−331-11-1−333−3−333−3−333−300000000000000000000
χ7222-2-2-2-222-1-2-22-2-22-222-222-111-111-11-1-11-111-11-1-11-2200000000-221-11-1−333−31-11-13−3−333−3−333−3−3300000000000000000000
χ7322-2-2-2-222-1-2-2-222-22-2-2222-111-111-11-1-111-1-11-111-12-200000000-22-11-113−33−31-11-1−33−333−3−33−333−300000000000000000000
χ7422-2-2-2-222-1-2-2-222-22-2-2222-111-111-11-1-111-1-11-111-12-200000000-22-11-11−33−331-11-13−33−3−333−33−3−3300000000000000000000
χ7522-2-2-2-222-1-2-2-222-22-2-2222-111-111-11-1-111-1-11-111-1-22000000002-21-11-13−33−3-11-11−33−33−333−33−3−3300000000000000000000
χ7622-2-2-2-222-1-2-2-222-22-2-2222-111-111-11-1-111-1-11-111-1-22000000002-21-11-1−33−33-11-113−33−33−3−33−333−300000000000000000000
χ77444-44-4-4-4-24-44i4i−4i−4i4i4i−4i−4i4-4-2-222-222-2-222−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ78444-44-4-4-4-24-4−4i−4i4i4i−4i−4i4i4i4-4-2-222-222-2-2222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ79444-44-4-4-4-2-444i4i−4i−4i−4i−4i4i4i-44-2-222-22222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ80444-44-4-4-4-2-44−4i−4i4i4i4i4i−4i−4i-44-2-222-22222-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ8144-44-44-4-4-24-44i−4i4i−4i4i−4i4i−4i-44-22-222-22-22-22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000000000000000
χ8244-44-44-4-4-24-4−4i4i−4i4i−4i4i−4i4i-44-22-222-22-22-222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000000000
χ8344-44-44-4-4-2-444i−4i4i−4i−4i4i−4i4i4-4-22-222-222-22-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000000000000000
χ8444-44-44-4-4-2-44−4i4i−4i4i4i−4i4i−4i4-4-22-222-222-22-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000000000000000000000
χ854-444-4-44-44000000000000-4444-4-4-40000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ864-444-4-44-44000000000000-4444-4-4-400000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ874-44-4-44-444000000000000-44-4-4-44400000000000000000000000000000000000000000000000022−2222−220000000000000000
χ884-44-4-44-444000000000000-44-4-4-444000000000000000000000000000000000000000000000000−2222−22220000000000000000
χ894-4-444-4-444000000000000-4-44-44-44000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ904-4-444-4-444000000000000-4-44-44-440000000000000000000000000000000000000000000000000000−222222−22000000000000
χ914-4-4-4444-44000000000000-4-4-4444-400000000000000000000000000000000000000000000000022−22−22220000000000000000
χ924-4-4-4444-44000000000000-4-4-4444-4000000000000000000000000000000000000000000000000−222222−220000000000000000
χ938-888-8-88-8-40000000000004-4-4-444400000000000000000000000000000000000000000000000000000000000000000000
χ948-88-8-88-88-40000000000004-4444-4-400000000000000000000000000000000000000000000000000000000000000000000
χ958-8-888-8-88-400000000000044-44-44-400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-8-8888-8-4000000000000444-4-4-4400000000000000000000000000000000000000000000000000000000000000000000

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