Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#12982 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | #120 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1869 |
| prime radical | C13×#532 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C22×C8×C13 ◁ G | |
474 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)(14,15,19,25,20,26,38,44,21,24,39,43,18,23,28,41)(16,27,31,36,29,42,45,17,30,33,37,32,35,22,40,34);(14,16,28,45,18,35,39,31,21,30,38,40,20,29,19,37)(15,22,41,36,23,33,43,34,24,42,44,32,26,27,25,17);(14,17)(15,16)(18,36)(19,27)(20,32)(21,34)(22,28)(23,35)(24,30)(25,37)(26,29)(31,43)(33,39)(38,42)(40,44)(41,45)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5970);