Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#12740 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1786 |
| prime radical | C2×C13×#575 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C22×C13×M16 ◁ G | |
914 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)(14,15,18,23,20,24,19,34)(16,25,28,42,27,41,35,39)(17,29,32,40,31,44,33,22)(21,30,37,43,36,45,38,26);(14,16)(15,21)(17,30)(18,28)(19,35)(20,27)(22,39)(23,37)(24,36)(25,29)(26,33)(31,45)(32,43)(34,38)(40,42)(41,44);(17,31)(22,40)(25,41)(26,43)(29,44)(30,45)(32,33)(39,42)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5728);