Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11549 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13093 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#99 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C22×Q8 | C23×C13 |
| prime radical | C13×#2431 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C22×C13×#41 ◁ G | |
752 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)(18,19,24,25,23,27,21,31)(20,28,26,33,32,22,30,29);(18,20,29,19,23,32,33,27)(21,30,28,25,24,26,22,31);(15,17)(18,21,23,24)(19,25,27,31)(20,30,32,26)(22,29,28,33)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6081);