Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#10831 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #381 |
| commutator | C23 | C2×C42×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C2×C13 | #1434 |
| prime radical | C24×C13 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C23×C4×C13 ◁ G | |
628 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)(16,24,26,20)(17,28)(18,23)(19,22)(21,29)(25,32,38,36)(27,37,40,33)(30,41)(31,35)(34,42)(39,43,45,44);(14,16,18,27,19,26,31,40)(15,20,23,33,22,24,35,37)(17,25,30,39,29,38,42,45)(21,32,34,43,28,36,41,44);(14,17)(15,21,22,28)(16,25)(18,30)(19,29)(20,32,24,36)(23,34,35,41)(26,38)(27,39)(31,42)(33,43,37,44)(40,45)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3819);