Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11521 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12805 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #410 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×#41 | C23×C13 |
| socle | C2×C13 | #1799 |
| prime radical | C13×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C2×C8×C13 ◁ C2×C13×#131 ◁ G | |
434 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,24)(17,28)(18,31,32,21)(19,23)(20,25)(22,30)(26,40,41,36)(27,37)(29,35,43,42)(33,38,44,45)(34,39);(14,16,17,25,19,27,30,39)(15,20,22,24,23,34,28,37)(18,26,29,38,32,41,43,45)(21,33,35,36,31,44,42,40);(15,21)(20,33)(22,35)(23,31)(24,36)(28,42)(34,44)(37,40)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5793);