Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11234 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#13269 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #391 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1985 |
| prime radical | C23×C13 | C2×M16 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C8×C13 ◁ G | |
308 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)(14,15,20,16,19,24,37,28,21,25,38,29,18,23,36,27)(17,30,33,42,32,22,39,26,34,40,44,31,35,41,45,43);(14,16,20,23,19,28,37,15,21,29,38,24,18,27,36,25)(17,31,44,41,32,43,45,30,34,42,33,22,35,26,39,40);(14,17,19,32,21,34,18,35)(15,22,23,30,25,41,24,40)(16,26,27,42,29,43,28,31)(20,33,37,39,38,44,36,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6257);