Finite Group Databasebeta

← Group #10591471

Character table — Group #10591471

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size111122222222224444444444444466666688888888121212121212121212121212121212242424363672
order1222334466666622366666661212121244121212126666661212444881212121212122424242441212882
χ1111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-11111111-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ511111111111111-1-11-1-1-1-11111111111111-1-1-1-1-1-1111-1-11111-1-1-1-11111-1-1-111-1
χ611111111111111-1-11-1-1-1-11111111111111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1111-1-11
χ711111111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-111111111-1-1-1-1-11
χ811111111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1-111111-1
χ9222222-2-22222220020000222-2-2-2-2222222000000-2-2-20000-2-200000000000000
χ10222222-2-22222220020000222-2-2-2-2-2-2-2-2-2-2000000-2-2200002200000000000000
χ1122222-12222-1-12-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-122200-1-1-1-1-1-10000000000
χ1222222-12222-1-12-122-1-1-1-1-1-1-1-1-1-122-2-2111122-1-1-1-1-1-1-2-2-2001111110000000000
χ1322222-12222-1-12-1-2-2-11111-1-1-1-1-12222-1-1-1-1-2-21111-1-12-2-200-1-111110000000000
χ1422222-12222-1-12-1-2-2-11111-1-1-1-1-122-2-21111-2-21111-1-1-2220011-1-1-1-10000000000
χ1522222-1-2-222-1-12-100-1−i3−i3i3i3-1-1-111-2-222-1-1-1-100−i3−i3i3i311-2000011−i3−i3i3i30000000000
χ1622222-1-2-222-1-12-100-1−i3−i3i3i3-1-1-111-2-2-2-2111100−i3−i3i3i31120000-1-1i3i3−i3−i30000000000
χ1722222-1-2-222-1-12-100-1i3i3−i3−i3-1-1-111-2-222-1-1-1-100i3i3−i3−i311-2000011i3i3−i3−i30000000000
χ1822222-1-2-222-1-12-100-1i3i3−i3−i3-1-1-111-2-2-2-2111100i3i3−i3−i31120000-1-1−i3−i3i3i30000000000
χ192222-1222-1-122-1222-12222-1-1-122-1-1000000-1-1-1-1-1-1-1-100022000000-1-1-1-12-1-1000
χ202222-1222-1-122-1222-12222-1-1-122-1-1000000-1-1-1-1-1-1-1-1000-2-20000001111-211000
χ212222-1222-1-122-12-2-2-1-2-2-2-2-1-1-122-1-1000000111111-1-100022000000-1-1-1-1-211000
χ222222-1222-1-122-12-2-2-1-2-2-2-2-1-1-122-1-1000000111111-1-1000-2-200000011112-1-1000
χ2322-2-222002-2-22-2-200200002-2-200002i−2i2i2i−2i−2i00000000000−i2i2000000−i2−i2i2i20002−20
χ2422-2-222002-2-22-2-200200002-2-200002i−2i2i2i−2i−2i00000000000i2−i2000000i2i2−i2−i2000−220
χ2522-2-222002-2-22-2-200200002-2-20000−2i2i−2i−2i2i2i00000000000−i2i2000000−i2−i2i2i2000−220
χ2622-2-222002-2-22-2-200200002-2-20000−2i2i−2i−2i2i2i00000000000i2−i2000000i2i2−i2−i20002−20
χ272-22-2222-2-2-22-22-20020000-2-222-22-20000000000002-202i−2i00002i−2i2i−2i0000000000
χ282-22-2222-2-2-22-22-20020000-2-222-22-20000000000002-20−2i2i0000−2i2i−2i2i0000000000
χ292-22-222-22-2-22-22-22-222-22-2-2-22-22-220000002-22-22-2-22000000000000000000000
χ302-22-222-22-2-22-22-2-222-22-22-2-22-22-22000000-22-22-22-22000000000000000000000
χ312-22-22-12-2-2-2-112100-1−i3i3i3−i311-1-112-2003−33−300−i3i3i3−i3-1102i−2i003−3−ii−ii0000000000
χ322-22-22-12-2-2-2-112100-1−i3i3i3−i311-1-112-200−33−3300−i3i3i3−i3-110−2i2i00−33i−ii−i0000000000
χ332-22-22-12-2-2-2-112100-1i3−i3−i3i311-1-112-2003−33−300i3−i3−i3i3-110−2i2i003−3i−ii−i0000000000
χ342-22-22-12-2-2-2-112100-1i3−i3−i3i311-1-112-200−33−3300i3−i3−i3i3-1102i−2i00−33−ii−ii0000000000
χ352-22-22-1-22-2-2-11212-2-1-11-1111-11-1-22003−33−32-2-11-111-100000−333−3−330000000000
χ362-22-22-1-22-2-2-11212-2-1-11-1111-11-1-2200−33−332-2-11-111-1000003−3−333−30000000000
χ372-22-22-1-22-2-2-1121-22-11-11-111-11-1-22003−33−3-221-11-11-100000−33−333−30000000000
χ382-22-22-1-22-2-2-1121-22-11-11-111-11-1-2200−33−33-221-11-11-1000003−33−3−330000000000
χ392-22-2-12-22112-2-1-22-2-12-22-211-1-221-1000000-11-11-111-100000000000−i3i3−i3i30−i3i3000
χ402-22-2-12-22112-2-1-22-2-12-22-211-1-221-1000000-11-11-111-100000000000i3−i3i3−i30i3−i3000
χ412-22-2-12-22112-2-1-2-22-1-22-2211-1-221-10000001-11-11-11-100000000000−i3i3−i3i30i3−i3000
χ422-22-2-12-22112-2-1-2-22-1-22-2211-1-221-10000001-11-11-11-100000000000i3−i3i3−i30−i3i3000
χ434444-24-4-4-2-244-2400-20000-2-2-2-4-42200000000000022000000000000000000000
χ444444-2-244-2-2-2-2-2-2441-2-2-2-2111-2-2-2-2000000-2-2111111000000000000000000000
χ454444-2-244-2-2-2-2-2-2-4-412222111-2-2-2-200000022-1-1-1-111000000000000000000000
χ464444-2-2-4-4-2-2-2-2-2-2001−2i3−2i32i32i3111222200000000i3i3−i3−i3-1-1000000000000000000000
χ474444-2-2-4-4-2-2-2-2-2-20012i32i3−2i3−2i3111222200000000−i3−i3i3i3-1-1000000000000000000000
χ4844-4-44-2004-42-2-4200-20000-22200004i−4i−2i−2i2i2i00000000000000000000000000000
χ4944-4-44-2004-42-2-4200-20000-2220000−4i4i2i2i−2i−2i00000000000000000000000000000
χ5044-4-4-2400-22-442-400-20000-222000000000000000000000−2i22i2000000i2i2−i2−i2000000
χ5144-4-4-2400-22-442-400-20000-2220000000000000000000002i2−2i2000000−i2−i2i2i2000000
χ524-44-4-244-4224-4-2-400-2000022-24-4-22000000000000-22000000000000000000000
χ534-44-4-2-24-422-22-22001−2i32i32i3−2i3-1-11-22-2200000000i3−i3−i3i31-1000000000000000000000
χ544-44-4-2-24-422-22-220012i3−2i3−2i32i3-1-11-22-2200000000−i3i3i3−i31-1000000000000000000000
χ554-44-4-2-2-4422-22-224-41-22-22-1-112-22-2000000-221-11-1-11000000000000000000000
χ564-44-4-2-2-4422-22-22-4412-22-2-1-112-22-20000002-2-11-11-11000000000000000000000
χ574-4-444400-44-4-4-440040000-44-4000000000000000000000000000000000000000
χ584-4-444-200-4422-4-200-200002-22000000−2i32i32i3−2i300000000000000000000000000000
χ594-4-444-200-4422-4-200-200002-220000002i3−2i3−2i32i300000000000000000000000000000
χ604-4-44-24002-2-4-42400-200002-22000000000000000000000000000006−6−66000000
χ614-4-44-24002-2-4-42400-200002-2200000000000000000000000000000−666−6000000
χ6288-8-8-4-400-444-44400200002-2-2000000000000000000000000000000000000000
χ638-8-88-4-4004-4444-40020000-22-2000000000000000000000000000000000000000

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