Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8534 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#8536 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #379 |
| commutator | C24 | C22×C4×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| prime radical | C13×#3496 | C2 |
| LCS | G ▷ C24 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1074 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,19,17,18,20,21)(26,29);(15,18)(16,20)(22,23)(24,26)(25,27)(28,29);(22,24)(23,26)(25,28)(27,29)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1524);