Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11867 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#11872 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1519 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C2×M16 | C23×C13 |
| prime radical | C13×#3060 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#131 ◁ G | |
372 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)(14,15,18,24,20,26,19,25)(16,27,30,22,31,40,28,41)(17,21,34,37,35,38,32,23)(29,42,44,36,33,39,45,43);(15,21)(16,28)(17,32)(18,19)(22,39)(23,25)(24,37)(26,38)(27,36)(30,31)(34,35)(40,43)(41,42)(44,45);(14,16,19,28,20,31,18,30)(15,22,24,40,26,41,25,27)(17,33,34,45,35,29,32,44)(21,36,23,42,38,43,37,39)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 4860);