Finite Group Databasebeta

← Group #10824479

Character table — Group #10824479

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order1222222234444444444446666666121212121212121212121212222244446666666688881212121212121212242424242424242488888888224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1
χ911111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-111-1-1-1-11-1
χ1011111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-11-1-11111-11
χ1111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1111-1-111-11
χ1211111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111111-1-1-111-1-11-1
χ1311111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-11-1-111-1-1-11
χ1411111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-111-1-1111-1
χ1511111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-11-1-1-111111-1
χ1611111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1111111-1111-1-1-1-1-11
χ17222222222-2-22222-2-2-2-2-2-22222222-2-22222-2-2-2-2-2-200000000000000000000000000000000000000000000002-2000000-22
χ18222222222-2-22222-2-2-2-2-2-22222222-2-22222-2-2-2-2-2-20000000000000000000000000000000000000000000000-220000002-2
χ19222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-22222-2-2000000000000000000000000000000000000000000000022000000-2-2
χ20222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-22222-2-20000000000000000000000000000000000000000000000-2-200000022
χ2122222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-11111-2-2-2-2-1-1-1-111111111111100000000000000000000
χ2322222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-1-2-2-2-21111-1-1-1-11111111100000000000000000000
χ2422222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111222211111111-1-1-1-1-1-1-1-100000000000000000000
χ2522222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-111111111-1-12222-2-2-2-2-1-1-1-1-1-1-1-122-2-211111111-1-1-1-1111100000000000000000000
χ2622222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-111111111-1-122-2-2-2-222-1-1-1-11111-2-2221111-1-1-1-11111-1-1-1-100000000000000000000
χ2722222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-111111111-1-1-2-22222-2-21111-1-1-1-1-2-222-1-1-1-111111111-1-1-1-100000000000000000000
χ2822222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-111111111-1-1-2-2-2-222221111111122-2-2-1-1-1-1-1-1-1-1-1-1-1-1111100000000000000000000
χ29222-2-22-2-222222-2-222-2-2-2-2-2-2-2-22222222-2-222-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ30222-2-22-2-222222-2-222-2-2-2-2-2-2-2-22222222-2-222-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ31222-2-22-2-2222-2-222-2-222-2-2-2-2-2-222222-2-222-2-222-2-20000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ32222-2-22-2-2222-2-222-2-222-2-2-2-2-2-222222-2-222-2-222-2-2000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ33222-2-22-2-22-2-222-2-2-2-22222-2-2-2-2222-2-222-2-2-2-22222002-2002-2000022-2-20000000022-2-20000000000000000000000000000
χ34222-2-22-2-22-2-222-2-2-2-22222-2-2-2-2222-2-222-2-2-2-2222200-2200-220000-2-22200000000-2-2220000000000000000000000000000
χ35222-2-22-2-22-2-2-2-22222-2-222-2-2-2-2222-2-2-2-22222-2-222002-200-22000022-2-200000000-2-2220000000000000000000000000000
χ36222-2-22-2-22-2-2-2-22222-2-222-2-2-2-2222-2-2-2-22222-2-22200-22002-20000-2-2220000000022-2-20000000000000000000000000000
χ37222-2-22-2-2-1-2-222-2-2-2-222221111-1-1-111-1-11111-1-1-1-1002-2002-2−i3−i3i3i3-1-1110000−i3−i3i3i3-1-111−i3−i3i3i3−i3−i3i3i300000000000000000000
χ38222-2-22-2-2-1-2-222-2-2-2-222221111-1-1-111-1-11111-1-1-1-1002-2002-2i3i3−i3−i3-1-1110000i3i3−i3−i3-1-111i3i3−i3−i3i3i3−i3−i300000000000000000000
χ39222-2-22-2-2-1-2-222-2-2-2-222221111-1-1-111-1-11111-1-1-1-100-2200-22−i3−i3i3i311-1-10000−i3−i3i3i311-1-1i3i3−i3−i3i3i3−i3−i300000000000000000000
χ40222-2-22-2-2-1-2-222-2-2-2-222221111-1-1-111-1-11111-1-1-1-100-2200-22i3i3−i3−i311-1-10000i3i3−i3−i311-1-1−i3−i3i3i3−i3−i3i3i300000000000000000000
χ41222-2-22-2-2-1-2-2-2-22222-2-2221111-1-1-11111-1-1-1-111-1-1002-200-22−i3−i3i3i3-1-1110000i3i3−i3−i311-1-1−i3−i3i3i3i3i3−i3−i300000000000000000000
χ42222-2-22-2-2-1-2-2-2-22222-2-2221111-1-1-11111-1-1-1-111-1-1002-200-22i3i3−i3−i3-1-1110000−i3−i3i3i311-1-1i3i3−i3−i3−i3−i3i3i300000000000000000000
χ43222-2-22-2-2-1-2-2-2-22222-2-2221111-1-1-11111-1-1-1-111-1-100-22002-2−i3−i3i3i311-1-10000i3i3−i3−i3-1-111i3i3−i3−i3−i3−i3i3i300000000000000000000
χ44222-2-22-2-2-1-2-2-2-22222-2-2221111-1-1-11111-1-1-1-111-1-100-22002-2i3i3−i3−i311-1-10000−i3−i3i3i3-1-111−i3−i3i3i3i3i3−i3−i300000000000000000000
χ4522-22-2-22-222-22i−2i2i−2i2i−2i2i−2i2-222-2-22-2-22-22i−2i2i−2i2i−2i2i−2i2-2000000000000000000000000000000000000000000002-20000002i−2i00
χ4622-22-2-22-222-22i−2i2i−2i2i−2i2i−2i2-222-2-22-2-22-22i−2i2i−2i2i−2i2i−2i2-200000000000000000000000000000000000000000000-22000000−2i2i00
χ4722-22-2-22-222-2−2i2i−2i2i−2i2i−2i2i2-222-2-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-2000000000000000000000000000000000000000000002-2000000−2i2i00
χ4822-22-2-22-222-2−2i2i−2i2i−2i2i−2i2i2-222-2-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-200000000000000000000000000000000000000000000-220000002i−2i00
χ4922-22-2-22-22-222i−2i2i−2i−2i2i−2i2i-2222-2-22-2-2-222i−2i2i−2i−2i2i−2i2i-222-2002i−2i002-22-2000000002i−2i2i−2i00000000000000000000000000000000
χ5022-22-2-22-22-222i−2i2i−2i−2i2i−2i2i-2222-2-22-2-2-222i−2i2i−2i−2i2i−2i2i-22-2200−2i2i00-22-2200000000−2i2i−2i2i00000000000000000000000000000000
χ5122-22-2-22-22-22−2i2i−2i2i2i−2i2i−2i-2222-2-22-2-2-22−2i2i−2i2i2i−2i2i−2i-222-200−2i2i002-22-200000000−2i2i−2i2i00000000000000000000000000000000
χ5222-22-2-22-22-22−2i2i−2i2i2i−2i2i−2i-2222-2-22-2-2-22−2i2i−2i2i2i−2i2i−2i-22-22002i−2i00-22-22000000002i−2i2i−2i00000000000000000000000000000000
χ5322-22-2-22-2-1-222i−2i2i−2i−2i2i−2i2i-22-1-111-1111-1−ii−iii−ii−i1-12-2002i−2i00-11-11−i3i3−i3i30000−ii−ii3−33−3−i3i3−i3i33−33−300000000000000000000
χ5422-22-2-22-2-1-222i−2i2i−2i−2i2i−2i2i-22-1-111-1111-1−ii−iii−ii−i1-12-2002i−2i00-11-11i3−i3i3−i30000−ii−ii−33−33i3−i3i3−i3−33−3300000000000000000000
χ5522-22-2-22-2-1-222i−2i2i−2i−2i2i−2i2i-22-1-111-1111-1−ii−iii−ii−i1-1-2200−2i2i001-11-1−i3i3−i3i30000i−ii−i3−33−3i3−i3i3−i3−33−3300000000000000000000
χ5622-22-2-22-2-1-222i−2i2i−2i−2i2i−2i2i-22-1-111-1111-1−ii−iii−ii−i1-1-2200−2i2i001-11-1i3−i3i3−i30000i−ii−i−33−33−i3i3−i3i33−33−300000000000000000000
χ5722-22-2-22-2-1-22−2i2i−2i2i2i−2i2i−2i-22-1-111-1111-1i−ii−i−ii−ii1-12-200−2i2i00-11-11−i3i3−i3i30000i−ii−i−33−33−i3i3−i3i3−33−3300000000000000000000
χ5822-22-2-22-2-1-22−2i2i−2i2i2i−2i2i−2i-22-1-111-1111-1i−ii−i−ii−ii1-12-200−2i2i00-11-11i3−i3i3−i30000i−ii−i3−33−3i3−i3i3−i33−33−300000000000000000000
χ5922-22-2-22-2-1-22−2i2i−2i2i2i−2i2i−2i-22-1-111-1111-1i−ii−i−ii−ii1-1-22002i−2i001-11-1−i3i3−i3i30000−ii−ii−33−33i3−i3i3−i33−33−300000000000000000000
χ6022-22-2-22-2-1-22−2i2i−2i2i2i−2i2i−2i-22-1-111-1111-1i−ii−i−ii−ii1-1-22002i−2i001-11-1i3−i3i3−i30000−ii−ii3−33−3−i3i3−i3i3−33−3300000000000000000000
χ6122-2-22-2-2222-22i−2i−2i2i2i−2i−2i2i-22-2-2222-2-22-22i−2i−2i2i2i−2i−2i2i-2200000000000000002-22i−2i000000002-2-222i−2i−2i2i00000000000000000000
χ6222-2-22-2-2222-22i−2i−2i2i2i−2i−2i2i-22-2-2222-2-22-22i−2i−2i2i2i−2i−2i2i-220000000000000000-22−2i2i00000000-222-2−2i2i2i−2i00000000000000000000
χ6322-2-22-2-2222-2−2i2i2i−2i−2i2i2i−2i-22-2-2222-2-22-2−2i2i2i−2i−2i2i2i−2i-2200000000000000002-2−2i2i000000002-2-22−2i2i2i−2i00000000000000000000
χ6422-2-22-2-2222-2−2i2i2i−2i−2i2i2i−2i-22-2-2222-2-22-2−2i2i2i−2i−2i2i2i−2i-220000000000000000-222i−2i00000000-222-22i−2i−2i2i00000000000000000000
χ6522-2-22-2-222-222i−2i−2i2i−2i2i2i−2i2-2-2-2222-2-2-222i−2i−2i2i−2i2i2i−2i2-200000000000000000000000000000000000022-2-22i2i−2i−2i000000000000
χ6622-2-22-2-222-222i−2i−2i2i−2i2i2i−2i2-2-2-2222-2-2-222i−2i−2i2i−2i2i2i−2i2-2000000000000000000000000000000000000-2-222−2i−2i2i2i000000000000
χ6722-2-22-2-222-22−2i2i2i−2i2i−2i−2i2i2-2-2-2222-2-2-22−2i2i2i−2i2i−2i−2i2i2-200000000000000000000000000000000000022-2-2−2i−2i2i2i000000000000
χ6822-2-22-2-222-22−2i2i2i−2i2i−2i−2i2i2-2-2-2222-2-2-22−2i2i2i−2i2i−2i−2i2i2-2000000000000000000000000000000000000-2-2222i2i−2i−2i000000000000
χ6922-2-22-2-22-12-22i−2i−2i2i2i−2i−2i2i-2211-1-1-111-11−iii−i−iii−i1-100000000−i3i3i3−i3−i3i3i3−i32-22i−2i3−3−333−3−33-111-1−iii−i00000000000000000000
χ7022-2-22-2-22-12-22i−2i−2i2i2i−2i−2i2i-2211-1-1-111-11−iii−i−iii−i1-100000000−i3i3i3−i3i3−i3−i3i3-22−2i2i3−3−33−333−31-1-11i−i−ii00000000000000000000
χ7122-2-22-2-22-12-22i−2i−2i2i2i−2i−2i2i-2211-1-1-111-11−iii−i−iii−i1-100000000i3−i3−i3i3−i3i3i3−i3-22−2i2i−333−33−3−331-1-11i−i−ii00000000000000000000
χ7222-2-22-2-22-12-22i−2i−2i2i2i−2i−2i2i-2211-1-1-111-11−iii−i−iii−i1-100000000i3−i3−i3i3i3−i3−i3i32-22i−2i−333−3−333−3-111-1−iii−i00000000000000000000
χ7322-2-22-2-22-12-2−2i2i2i−2i−2i2i2i−2i-2211-1-1-111-11i−i−iii−i−ii1-100000000−i3i3i3−i3−i3i3i3−i32-2−2i2i−333−3−333−3-111-1i−i−ii00000000000000000000
χ7422-2-22-2-22-12-2−2i2i2i−2i−2i2i2i−2i-2211-1-1-111-11i−i−iii−i−ii1-100000000−i3i3i3−i3i3−i3−i3i3-222i−2i−333−33−3−331-1-11−iii−i00000000000000000000
χ7522-2-22-2-22-12-2−2i2i2i−2i−2i2i2i−2i-2211-1-1-111-11i−i−iii−i−ii1-100000000i3−i3−i3i3−i3i3i3−i3-222i−2i3−3−33−333−31-1-11−iii−i00000000000000000000
χ7622-2-22-2-22-12-2−2i2i2i−2i−2i2i2i−2i-2211-1-1-111-11i−i−iii−i−ii1-100000000i3−i3−i3i3i3−i3−i3i32-2−2i2i3−3−333−3−33-111-1i−i−ii00000000000000000000
χ7744444444-2-4-44444-4-4-4-4-4-4-2-2-2-2-2-2-222-2-2-2-222222200000000000000000000000000000000000000000000000000000000
χ7844444444-2-4-4-4-4-4-44444-4-4-2-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000000000000000000000000000000000000
χ79444-4-44-4-4-24444-4-444-4-4-4-42222-2-2-2-2-2-2-222-2-2222200000000000000000000000000000000000000000000000000000000
χ80444-4-44-4-4-244-4-444-4-444-4-42222-2-2-2-2-222-2-222-2-22200000000000000000000000000000000000000000000000000000000
χ8144-44-4-44-4-24-44i−4i4i−4i4i−4i4i−4i4-4-2-222-222-22−2i2i−2i2i−2i2i−2i2i-2200000000000000000000000000000000000000000000000000000000
χ8244-44-4-44-4-24-4−4i4i−4i4i−4i4i−4i4i4-4-2-222-222-222i−2i2i−2i2i−2i2i−2i-2200000000000000000000000000000000000000000000000000000000
χ8344-4-44-4-44-2-444i−4i−4i4i−4i4i4i−4i4-422-2-2-2222-2−2i2i2i−2i2i−2i−2i2i-2200000000000000000000000000000000000000000000000000000000
χ8444-4-44-4-44-2-44−4i4i4i−4i4i−4i−4i4i4-422-2-2-2222-22i−2i−2i2i−2i2i2i−2i-2200000000000000000000000000000000000000000000000000000000
χ854-4444-4-4-440000000000004-44-4-44-40000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ864-4444-4-4-440000000000004-44-4-44-400000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ874-44-4-4-4444000000000000-44-44-44-400000000000000000000000000000000000000000000000022−2222−220000000000000000
χ884-44-4-4-4444000000000000-44-44-44-4000000000000000000000000000000000000000000000000−2222−22220000000000000000
χ894-4-44-44-4440000000000004-4-44-4-4400000000000000000000000000000000000000000000000022−22−22220000000000000000
χ904-4-44-44-4440000000000004-4-44-4-44000000000000000000000000000000000000000000000000−222222−220000000000000000
χ914-4-4-4444-44000000000000-444-4-4-44000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ924-4-4-4444-44000000000000-444-4-4-440000000000000000000000000000000000000000000000000000−222222−22000000000000
χ938-8888-8-8-8-4000000000000-44-444-4400000000000000000000000000000000000000000000000000000000000000000000
χ948-88-8-8-888-40000000000004-44-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ958-8-88-88-88-4000000000000-444-444-400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-8-8888-8-40000000000004-4-4444-400000000000000000000000000000000000000000000000000000000000000000000

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