Finite Group Databasebeta

← Group #11713679

Character table — Group #11713679

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222444466668888888812121212121212121212161616161616161616161616242424242424242424244848
order12222222444444444444366666664488888888121212121212121212121212444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1
χ3111111111111-1-1-1-11111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ511111111-1-1-1-111-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-11-1
χ611111111-1-1-1-111-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-11-1-111-11
χ711111111-1-1-1-1-1-111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-1-1-111-11
χ811111111-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-111-1-11-1
χ922222222222222222222-1-1-1-1-1-1-1-12200000000-1-1-1-1-1-1-1-1-1-1-1-1000022000000
χ10222222222222-2-2-2-22222-1-1-1-1-1-1-1-122000000001111-1-1-1-111110000-2-2000000
χ1122222222-2-2-2-222-2-22222-1-1-1-1-1-1-1-1-2-20000000011111111-1-1-1-10000-22000000
χ1222222222-2-2-2-2-2-2222222-1-1-1-1-1-1-1-1-2-200000000-1-1-1-11111111100002-2000000
χ1322-222-2-2-20000000022-2-22222-2-2-2-200000022-2-2000000000000002-200000000
χ1422-222-2-2-20000000022-2-22222-2-2-2-2000000-2-22200000000000000-2200000000
χ1522-2-2-22-222i2i−2i−2i2i−2i2-20000-111-11-1-1100−i2−i2i2i22−22−211-1-1ii−i−iii−i−i0000002−2−i2i200
χ1622-2-2-22-222i2i−2i−2i2i−2i2-20000-111-11-1-1100i2i2−i2−i2−22−2211-1-1ii−i−iii−i−i000000−22i2−i200
χ1722-2-2-22-222i2i−2i−2i−2i2i-220000-111-11-1-1100−i2−i2i2i22−22−2-1-111ii−i−i−i−iii000000−22i2−i200
χ1822-2-2-22-222i2i−2i−2i−2i2i-220000-111-11-1-1100i2i2−i2−i2−22−22-1-111ii−i−i−i−iii0000002−2−i2i200
χ1922-2-2-22-22−2i−2i2i2i2i−2i-220000-111-11-1-1100−i2−i2i2i2−22−22-1-111−i−iiiii−i−i0000002−2i2−i200
χ2022-2-2-22-22−2i−2i2i2i2i−2i-220000-111-11-1-1100i2i2−i2−i22−22−2-1-111−i−iiiii−i−i000000−22−i2i200
χ2122-2-2-22-22−2i−2i2i2i−2i2i2-20000-111-11-1-1100−i2−i2i2i2−22−2211-1-1−i−iii−i−iii000000−22−i2i200
χ2222-2-2-22-22−2i−2i2i2i−2i2i2-20000-111-11-1-1100i2i2−i2−i22−22−211-1-1−i−iii−i−iii0000002−2i2−i200
χ232-222-22-2-2000000002-22-222-2-222-2-2002-22-200000000000000002-20000000000
χ242-222-22-2-2000000002-22-222-2-222-2-200-22-220000000000000000-220000000000
χ252-2-22-2-2222-22-200002-2-2222-2-2-2-2222-20000000000002-22-20000000000000000
χ262-2-22-2-2222-22-200002-2-22-1-11111-1-12-200000000−i3i3−i3i3-11-11−i3i3−i3i3000000000000
χ272-2-22-2-2222-22-200002-2-22-1-11111-1-12-200000000i3−i3i3−i3-11-11i3−i3i3−i3000000000000
χ282-2-22-2-222-22-2200002-2-2222-2-2-2-222-22000000000000-22-220000000000000000
χ292-2-22-2-222-22-2200002-2-22-1-11111-1-1-2200000000−i3i3−i3i31-11-1i3−i3i3−i3000000000000
χ302-2-22-2-222-22-2200002-2-22-1-11111-1-1-2200000000i3−i3i3−i31-11-1−i3i3−i3i3000000000000
χ313333333333333333-1-1-1-100000000-1-111111111000000000000-1-1-1-1-1-11111-1-1
χ323333333333333333-1-1-1-100000000-1-1-1-1-1-1-1-1-1-10000000000001111-1-1-1-1-1-111
χ33333333333333-3-3-3-3-1-1-1-100000000-1-111111111000000000000-1-1-1-111-1-1-1-111
χ34333333333333-3-3-3-3-1-1-1-100000000-1-1-1-1-1-1-1-1-1-10000000000001111111111-1-1
χ3533333333-3-3-3-333-3-3-1-1-1-100000000111111-1-1-1-1000000000000-1-1111-111-1-1-11
χ3633333333-3-3-3-333-3-3-1-1-1-10000000011-1-1-1-1111100000000000011-1-11-1-1-1111-1
χ3733333333-3-3-3-3-3-333-1-1-1-100000000111111-1-1-1-1000000000000-1-111-11-1-1111-1
χ3833333333-3-3-3-3-3-333-1-1-1-10000000011-1-1-1-1111100000000000011-1-1-1111-1-1-11
χ39444-4-4-44-4000000000000-222-2-222-200000022−22−2222000000000000000000000000
χ40444-4-4-44-4000000000000-222-2-222-2000000−222222−22000000000000000000000000
χ4144-444-4-4-40000000044-4-4-2-2-2-222220000000000000000000000000000000000
χ4244-4-4-44-444i4i−4i−4i4i−4i4-400001-1-11-111-10000000000-1-111−i−iii−i−iii000000000000
χ4344-4-4-44-444i4i−4i−4i−4i4i-4400001-1-11-111-1000000000011-1-1−i−iiiii−i−i000000000000
χ4444-4-4-44-44−4i−4i4i4i4i−4i-4400001-1-11-111-1000000000011-1-1ii−i−i−i−iii000000000000
χ4544-4-4-44-44−4i−4i4i4i−4i4i4-400001-1-11-111-10000000000-1-111ii−i−iii−i−i000000000000
χ464-444-44-4-4000000004-44-4-2-222-2-2220000000000000000000000000000000000
χ474-44-44-4-444i−4i−4i4i000000001-11-11-11-10000000000−i3i3i3−i3−iii−i3−3−33000000000000
χ484-44-44-4-444i−4i−4i4i000000001-11-11-11-10000000000i3−i3−i3i3−iii−i−333−3000000000000
χ494-44-44-4-444i−4i−4i4i00000000-22-22-22-22000000000000002i−2i−2i2i0000000000000000
χ504-44-44-4-44−4i4i4i−4i000000001-11-11-11-10000000000−i3i3i3−i3i−i−ii−333−3000000000000
χ514-44-44-4-44−4i4i4i−4i000000001-11-11-11-10000000000i3−i3−i3i3i−i−ii3−3−33000000000000
χ524-44-44-4-44−4i4i4i−4i00000000-22-22-22-2200000000000000−2i2i2i−2i0000000000000000
χ534-4-4-4444-4000000000000-22-222-22-200−2i22i22i2−2i20000000000000000000000000000
χ544-4-4-4444-4000000000000-22-222-22-2002i2−2i2−2i22i20000000000000000000000000000
χ5566-666-6-6-600000000-2-2220000000000000022-2-200000000000000-2200000000
χ5666-666-6-6-600000000-2-22200000000000000-2-222000000000000002-200000000
χ576-666-66-6-600000000-22-2200000000002-22-20000000000000000-220000000000
χ586-666-66-6-600000000-22-220000000000-22-2200000000000000002-20000000000
χ596-6-66-6-6666-66-60000-222-200000000-2200000000000000000000000000000000
χ606-6-66-6-666-66-660000-222-2000000002-200000000000000000000000000000000
χ61888-8-8-88-80000000000002-2-222-2-220000000000000000000000000000000000
χ628-8-8-8888-80000000000002-22-2-22-220000000000000000000000000000000000

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