Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61038 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| socle | C22×C13 | C23×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C4×D4×C13 ◁ G | |
2790 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,27)(21,25)(22,31)(23,26)(24,30)(28,29)(32,33);(18,20)(19,24)(21,30)(22,32)(23,28)(25,29)(26,33)(27,31);(15,17)(20,28)(24,33)(27,29)(30,32);(18,19)(20,29)(21,25)(22,31)(23,26)(24,32)(27,28)(30,33);(18,21,23,22)(19,25,26,31)(20,30,28,32)(24,29,33,27)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54026);