Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26953 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#121 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C4×C13×C22⋊C4 ◁ G | |
870 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)(15,16)(18,19)(20,24)(21,23)(22,25)(26,27,29,32)(28,34,36,31)(30,33,37,40)(35,41,38,39);(14,15,17,16)(18,20,21,25)(19,22,23,24)(28,35)(30,37)(31,39)(33,40)(34,41)(36,38);(19,23)(22,24)(26,28,29,36)(27,31,32,34)(30,38,37,35)(33,41,40,39);(14,16,17,15)(19,23)(22,24)(28,36)(31,34)(35,38)(39,41)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19941);