Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#21009 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #386 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | C2×#386 |
| prime radical | C13×#3449 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C23×C4×C13 ◁ G | |
1708 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,25)(17,30,32,22)(18,23)(19,33)(20,24)(21,28)(26,39,42,45)(27,36)(29,40)(31,38,34,37)(35,41,44,43);(14,16,19,28,20,29,18,27)(15,21,23,25,24,36,33,40)(17,26,34,43,32,42,31,41)(22,35,37,39,30,44,38,45);(14,17)(15,22)(16,26)(18,31)(19,34)(20,32)(21,35)(23,37)(24,30)(25,39)(27,41)(28,43)(29,42)(33,38)(36,44)(40,45);(14,18,20,19)(15,23,24,33)(16,27,29,28)(17,31,32,34)(21,25,36,40)(22,37,30,38)(26,41,42,43)(35,39,44,45)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 13997);