Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12605 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C2×C42 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | C2×#97 |
| prime radical | C24×C13 | M16 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ G | |
510 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)(19,24,25,27)(21,29)(26,33,32,31)(28,30);(15,17)(18,19,21,26,22,27,30,33,23,25,29,32,20,24,28,31);(19,24,25,27)(21,29)(26,33,32,31)(28,30)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5593);