Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12948 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12948 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1864 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
384 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)(15,21,24,23)(16,26,27,44)(17,29)(18,33)(19,32)(22,39)(25,34,36,30)(28,35,37,31)(38,45)(40,42);(14,15,19,36,20,24,32,25)(16,22,37,41,27,39,28,43)(17,30,29,21,18,34,33,23)(26,38,35,45,44,42,31,40);(14,16)(15,22)(17,31)(18,35)(19,37)(20,27)(21,38)(23,42)(24,39)(25,43)(26,29)(28,32)(30,40)(33,44)(34,45)(36,41)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5936);