Finite Group Databasebeta

← Group #10824556

Character table — Group #10824556

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order122222223444444444444666666612121212121212121212121244444444888812121212121212121212121212121212242424242424242488888888222244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ51111111111111111111111111111111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111
χ61111111111111111111111111111111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ911111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-1-1-1-1-1
χ1011111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-111111
χ1111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-11-11-1-111
χ1211111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-11-111-1-1
χ1311111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-11-1111-1-1
χ1411111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11-11-1-1-111
χ1511111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-11111
χ1611111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11-11-1-1-1-1
χ17222222222-2-22222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000022-2-20000
χ18222222222-2-22222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000-2-2220000
χ19222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-22222-2-20000000000000000000000000000000000000000000000002-2-220000
χ20222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-22222-2-2000000000000000000000000000000000000000000000000-222-20000
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
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000000000000000
χ2322222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ2422222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ2522222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-11111-1-11111-1-12222-2-2-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000000000000000
χ2622222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-11111-1-11111-1-122-2-222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ2722222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-11111-1-11111-1-1-2-222-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000000000000000
χ2822222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-11111-1-11111-1-1-2-2-2-2222222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ29222-22-2-2-222-22i2i−2i−2i2i2i−2i−2i2-22-2-22-22-22i2i−2i−2i2-22i2i−2i−2i2-200000000000000000000000000000000000022-2-22i2i−2i−2i000000000000
χ30222-22-2-2-222-22i2i−2i−2i2i2i−2i−2i2-22-2-22-22-22i2i−2i−2i2-22i2i−2i−2i2-2000000000000000000000000000000000000-2-222−2i−2i2i2i000000000000
χ31222-22-2-2-222-2−2i−2i2i2i−2i−2i2i2i2-22-2-22-22-2−2i−2i2i2i2-2−2i−2i2i2i2-200000000000000000000000000000000000022-2-2−2i−2i2i2i000000000000
χ32222-22-2-2-222-2−2i−2i2i2i−2i−2i2i2i2-22-2-22-22-2−2i−2i2i2i2-2−2i−2i2i2i2-2000000000000000000000000000000000000-2-2222i2i−2i−2i000000000000
χ33222-22-2-2-22-222i2i−2i−2i−2i−2i2i2i-222-2-22-22-22i2i−2i−2i-22−2i−2i2i2i-22000000002-22i−2i000000000000000022-2-22i2i−2i−2i00000000000000000000
χ34222-22-2-2-22-222i2i−2i−2i−2i−2i2i2i-222-2-22-22-22i2i−2i−2i-22−2i−2i2i2i-2200000000-22−2i2i0000000000000000-2-222−2i−2i2i2i00000000000000000000
χ35222-22-2-2-22-22−2i−2i2i2i2i2i−2i−2i-222-2-22-22-2−2i−2i2i2i-222i2i−2i−2i-22000000002-2−2i2i000000000000000022-2-2−2i−2i2i2i00000000000000000000
χ36222-22-2-2-22-22−2i−2i2i2i2i2i−2i−2i-222-2-22-22-2−2i−2i2i2i-222i2i−2i−2i-2200000000-222i−2i0000000000000000-2-2222i2i−2i−2i00000000000000000000
χ37222-22-2-2-2-1-222i2i−2i−2i−2i−2i2i2i-22-111-11-11−i−iii1-1ii−i−i1-1000000002-22i−2i−i3−i3i3i333−3−3−i3−i3i3i333−3−3-1-111−i−iii00000000000000000000
χ38222-22-2-2-2-1-222i2i−2i−2i−2i−2i2i2i-22-111-11-11−i−iii1-1ii−i−i1-1000000002-22i−2ii3i3−i3−i3−3−333i3i3−i3−i3−3−333-1-111−i−iii00000000000000000000
χ39222-22-2-2-2-1-222i2i−2i−2i−2i−2i2i2i-22-111-11-11−i−iii1-1ii−i−i1-100000000-22−2i2i−i3−i3i3i333−3−3i3i3−i3−i3−3−33311-1-1ii−i−i00000000000000000000
χ40222-22-2-2-2-1-222i2i−2i−2i−2i−2i2i2i-22-111-11-11−i−iii1-1ii−i−i1-100000000-22−2i2ii3i3−i3−i3−3−333−i3−i3i3i333−3−311-1-1ii−i−i00000000000000000000
χ41222-22-2-2-2-1-22−2i−2i2i2i2i2i−2i−2i-22-111-11-11ii−i−i1-1−i−iii1-1000000002-2−2i2i−i3−i3i3i3−3−333−i3−i3i3i3−3−333-1-111ii−i−i00000000000000000000
χ42222-22-2-2-2-1-22−2i−2i2i2i2i2i−2i−2i-22-111-11-11ii−i−i1-1−i−iii1-1000000002-2−2i2ii3i3−i3−i333−3−3i3i3−i3−i333−3−3-1-111ii−i−i00000000000000000000
χ43222-22-2-2-2-1-22−2i−2i2i2i2i2i−2i−2i-22-111-11-11ii−i−i1-1−i−iii1-100000000-222i−2i−i3−i3i3i3−3−333i3i3−i3−i333−3−311-1-1−i−iii00000000000000000000
χ44222-22-2-2-2-1-22−2i−2i2i2i2i2i−2i−2i-22-111-11-11ii−i−i1-1−i−iii1-100000000-222i−2ii3i3−i3−i333−3−3−i3−i3i3i3−3−33311-1-1−i−iii00000000000000000000
χ4522-22-22-2-222-22i−2i2i−2i2i−2i2i−2i-22-22-2-222-22i−2i2i−2i2-22i−2i2i−2i-2200000000000000000000000000000000000000000000002-20000002i−2i
χ4622-22-22-2-222-22i−2i2i−2i2i−2i2i−2i-22-22-2-222-22i−2i2i−2i2-22i−2i2i−2i-220000000000000000000000000000000000000000000000-22000000−2i2i
χ4722-22-22-2-222-2−2i2i−2i2i−2i2i−2i2i-22-22-2-222-2−2i2i−2i2i2-2−2i2i−2i2i-2200000000000000000000000000000000000000000000002-2000000−2i2i
χ4822-22-22-2-222-2−2i2i−2i2i−2i2i−2i2i-22-22-2-222-2−2i2i−2i2i2-2−2i2i−2i2i-220000000000000000000000000000000000000000000000-220000002i−2i
χ4922-22-22-2-22-222i−2i2i−2i−2i2i−2i2i2-2-22-2-222-22i−2i2i−2i-22−2i2i−2i2i2-22-200002i−2i0000000000002-22-22i−2i2i−2i0000000000000000000000000000
χ5022-22-22-2-22-222i−2i2i−2i−2i2i−2i2i2-2-22-2-222-22i−2i2i−2i-22−2i2i−2i2i2-2-220000−2i2i000000000000-22-22−2i2i−2i2i0000000000000000000000000000
χ5122-22-22-2-22-22−2i2i−2i2i2i−2i2i−2i2-2-22-2-222-2−2i2i−2i2i-222i−2i2i−2i2-22-20000−2i2i0000000000002-22-2−2i2i−2i2i0000000000000000000000000000
χ5222-22-22-2-22-22−2i2i−2i2i2i−2i2i−2i2-2-22-2-222-2−2i2i−2i2i-222i−2i2i−2i2-2-2200002i−2i000000000000-22-222i−2i2i−2i0000000000000000000000000000
χ5322-22-22-2-2-1-222i−2i2i−2i−2i2i−2i2i2-21-111-1-11−ii−ii1-1i−ii−i-112-200002i−2i00003−33−3−i3i3−i3i3-11-11−ii−ii3−33−3−i3i3−i3i300000000000000000000
χ5422-22-22-2-2-1-222i−2i2i−2i−2i2i−2i2i2-21-111-1-11−ii−ii1-1i−ii−i-112-200002i−2i0000−33−33i3−i3i3−i3-11-11−ii−ii−33−33i3−i3i3−i300000000000000000000
χ5522-22-22-2-2-1-222i−2i2i−2i−2i2i−2i2i2-21-111-1-11−ii−ii1-1i−ii−i-11-220000−2i2i00003−33−3−i3i3−i3i31-11-1i−ii−i−33−33i3−i3i3−i300000000000000000000
χ5622-22-22-2-2-1-222i−2i2i−2i−2i2i−2i2i2-21-111-1-11−ii−ii1-1i−ii−i-11-220000−2i2i0000−33−33i3−i3i3−i31-11-1i−ii−i3−33−3−i3i3−i3i300000000000000000000
χ5722-22-22-2-2-1-22−2i2i−2i2i2i−2i2i−2i2-21-111-1-11i−ii−i1-1−ii−ii-112-20000−2i2i00003−33−3i3−i3i3−i3-11-11i−ii−i3−33−3i3−i3i3−i300000000000000000000
χ5822-22-22-2-2-1-22−2i2i−2i2i2i−2i2i−2i2-21-111-1-11i−ii−i1-1−ii−ii-112-20000−2i2i0000−33−33−i3i3−i3i3-11-11i−ii−i−33−33−i3i3−i3i300000000000000000000
χ5922-22-22-2-2-1-22−2i2i−2i2i2i−2i2i−2i2-21-111-1-11i−ii−i1-1−ii−ii-11-2200002i−2i00003−33−3i3−i3i3−i31-11-1−ii−ii−33−33−i3i3−i3i300000000000000000000
χ6022-22-22-2-2-1-22−2i2i−2i2i2i−2i2i−2i2-21-111-1-11i−ii−i1-1−ii−ii-11-2200002i−2i0000−33−33−i3i3−i3i31-11-1−ii−ii3−33−3i3−i3i3−i300000000000000000000
χ6122-2-2-2-2222222-2-222-2-22-2-2-2-22-2-2222-2-22222-2-22-2-2002i−2i2i−2i0000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ6222-2-2-2-2222222-2-222-2-22-2-2-2-22-2-2222-2-22222-2-22-2-200−2i2i−2i2i000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ6322-2-2-2-222222-222-2-222-2-2-2-2-22-2-222-222-222-222-2-2-2002i−2i−2i2i0000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ6422-2-2-2-222222-222-2-222-2-2-2-2-22-2-222-222-222-222-2-2-200−2i2i2i−2i000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ6522-2-2-2-2222-2-22-2-22-222-222-2-22-2-2222-2-22-2-2-222-222000000000000000000000000000000000000000000002-20000002-200
χ6622-2-2-2-2222-2-22-2-22-222-222-2-22-2-2222-2-22-2-2-222-22200000000000000000000000000000000000000000000-22000000-2200
χ6722-2-2-2-2222-2-2-222-22-2-2222-2-22-2-222-222-2-2-22-2-2222000000000000000000000000000000000000000000002-2000000-2200
χ6822-2-2-2-2222-2-2-222-22-2-2222-2-22-2-222-222-2-2-22-2-222200000000000000000000000000000000000000000000-220000002-200
χ6922-2-2-2-222-1222-2-222-2-22-2-211-111-1-1-111-1-1-1-111-111002i−2i2i−2i000000−iii−ii−i−ii−i3i3i3−i3−i3i3i3−i33−3−33−333−300000000000000000000
χ7022-2-2-2-222-1222-2-222-2-22-2-211-111-1-1-111-1-1-1-111-111002i−2i2i−2i000000−iii−ii−i−iii3−i3−i3i3i3−i3−i3i3−333−33−3−3300000000000000000000
χ7122-2-2-2-222-1222-2-222-2-22-2-211-111-1-1-111-1-1-1-111-11100−2i2i−2i2i000000i−i−ii−iii−i−i3i3i3−i3−i3i3i3−i3−333−33−3−3300000000000000000000
χ7222-2-2-2-222-1222-2-222-2-22-2-211-111-1-1-111-1-1-1-111-11100−2i2i−2i2i000000i−i−ii−iii−ii3−i3−i3i3i3−i3−i3i33−3−33−333−300000000000000000000
χ7322-2-2-2-222-122-222-2-222-2-2-211-111-1-11-1-11-1-11-1-1111002i−2i−2i2i000000−iii−i−iii−i−i3i3i3−i3i3−i3−i3i33−3−333−3−3300000000000000000000
χ7422-2-2-2-222-122-222-2-222-2-2-211-111-1-11-1-11-1-11-1-1111002i−2i−2i2i000000−iii−i−iii−ii3−i3−i3i3−i3i3i3−i3−333−3−333−300000000000000000000
χ7522-2-2-2-222-122-222-2-222-2-2-211-111-1-11-1-11-1-11-1-111100−2i2i2i−2i000000i−i−iii−i−ii−i3i3i3−i3i3−i3−i3i3−333−3−333−300000000000000000000
χ7622-2-2-2-222-122-222-2-222-2-2-211-111-1-11-1-11-1-11-1-111100−2i2i2i−2i000000i−i−iii−i−iii3−i3−i3i3−i3i3i3−i33−3−333−3−3300000000000000000000
χ7744444444-2-4-44444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ7844444444-2-4-4-4-4-4-44444-4-4-2-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000000000000000000000000000000000000
χ79444-44-4-4-4-24-44i4i−4i−4i4i4i−4i−4i4-4-222-22-22−2i−2i2i2i-22−2i−2i2i2i-2200000000000000000000000000000000000000000000000000000000
χ80444-44-4-4-4-24-4−4i−4i4i4i−4i−4i4i4i4-4-222-22-222i2i−2i−2i-222i2i−2i−2i-2200000000000000000000000000000000000000000000000000000000
χ8144-44-44-4-4-24-44i−4i4i−4i4i−4i4i−4i-442-222-2-22−2i2i−2i2i-22−2i2i−2i2i2-200000000000000000000000000000000000000000000000000000000
χ8244-44-44-4-4-24-4−4i4i−4i4i−4i4i−4i4i-442-222-2-222i−2i2i−2i-222i−2i2i−2i2-200000000000000000000000000000000000000000000000000000000
χ8344-4-4-4-444-2-4-44-4-44-444-44422-222-2-2-222-2222-2-22-2-200000000000000000000000000000000000000000000000000000000
χ8444-4-4-4-444-2-4-4-444-44-4-444422-222-2-22-2-2222-222-2-2-200000000000000000000000000000000000000000000000000000000
χ854-444-4-4-44400000000000044-4-4-4-44000000000000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ864-444-4-4-44400000000000044-4-4-4-440000000000000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ874-44-4-444-440000000000004-44-44-4-4000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ884-44-4-444-440000000000004-44-44-4-40000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ894-4-444-44-44000000000000-4444-4-4-40000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ904-4-444-44-44000000000000-4444-4-4-400000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ914-4-4-444-444000000000000-4-4-444-44000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ924-4-4-444-444000000000000-4-4-444-440000000000000000000000000000000000000000000000000000−222222−22000000000000
χ938-888-8-8-88-4000000000000-4-44444-400000000000000000000000000000000000000000000000000000000000000000000
χ948-88-8-888-8-4000000000000-44-44-44400000000000000000000000000000000000000000000000000000000000000000000
χ958-8-888-88-8-40000000000004-4-4-444400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-8-888-88-4000000000000444-4-44-400000000000000000000000000000000000000000000000000000000000000000000

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