Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#10993 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #120 |
| commutator | C24 | C22×C4×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C22×C13 | #386 |
| prime radical | C2×C13×#525 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C4×C13 ◁ G | |
1458 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,21,25,22,24,30,32)(20,26,28,33,27,23,29,31);(15,17)(18,20)(19,23)(21,29)(22,27)(24,26)(25,33)(28,30)(31,32);(23,26)(31,33)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3981);