Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12850 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #117 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | #432 |
| prime radical | C24×C13 | M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#97 ◁ G | |
430 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,22,29,23,26,38,42,24,27,37,43,21,28,35,44)(20,30,33,45,34,39,47,48,31,25,36,40,32,41,46,49);(18,20)(19,25)(21,32)(22,36)(23,34)(24,31)(26,41)(27,30)(28,39)(29,45)(33,37)(35,47)(38,46)(40,43)(42,48)(44,49);(15,17)(19,26,27,28)(20,31)(22,37)(25,39,30,41)(29,44,43,42)(32,34)(35,38)(40,49,45,48)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5838);