Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#25914 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C13×#117 ◁ G | |
1010 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,22,25)(20,24,21,23)(28,34)(29,36)(31,37)(33,39)(35,40)(38,41);(14,15)(16,17)(18,20,22,21)(19,23,25,24)(26,27)(28,31)(29,33)(30,32)(34,37)(35,38)(36,39)(40,41);(15,17)(18,20,22,21)(19,24,25,23)(26,28,29,34,30,35,36,40)(27,31,33,37,32,38,39,41);(18,21,22,20)(19,24,25,23)(27,32)(31,38)(33,39)(37,41)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18902);