Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(7,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4×C13 · Schur multiplier (H2) = C214 |
| direct product | C13×#62654 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator | C2 | C25×C4×C13 |
| Frattini, cosocle | C22 | C26×C13 |
| prime radical | C2×C13×#585 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
11222 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(18,19)(20,24)(21,28)(22,23)(25,29)(26,30)(27,33)(31,32);(19,23)(24,30)(25,28)(31,33);(20,26)(24,30)(27,32)(31,33);(18,20)(19,24)(21,27)(22,26)(23,30)(25,31)(28,33)(29,32);(18,19)(20,24)(21,25)(22,23)(26,30)(27,31)(28,29)(32,33);(18,21,22,29)(19,25,23,28)(20,27,26,32)(24,31,30,33)1690 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55642);