Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13024 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1879 |
| prime radical | C13×#3414 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C2×C13×#97 ◁ G | |
466 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)(14,15,20,26,21,27,19,38,22,28,39,45,37,44,18,25)(16,29,30,42,31,43,17,33,32,24,35,23,34,40,36,41);(14,16,21,34,22,32,37,31)(15,23,27,33,28,42,44,41)(17,19,30,39,36,18,35,20)(24,25,43,26,29,38,40,45);(14,17)(15,24)(16,19)(18,32)(20,31)(21,30)(22,36)(23,25)(26,33)(27,43)(28,29)(34,39)(35,37)(38,42)(40,44)(41,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6012);