Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#10999 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #120 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C22×C13 | #379 |
| prime radical | C13×#3449 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C4×C13 ◁ G | |
1310 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)(18,19,23,27,24,28,22,35)(20,29,31,25,32,40,36,39)(21,26,33,42,34,43,37,41)(30,45,48,49,47,44,46,38);(14,15)(16,17)(18,20)(19,25)(21,30)(22,36)(23,31)(24,32)(26,38)(27,40)(28,39)(29,35)(33,48)(34,47)(37,46)(41,44)(42,45)(43,49);(15,17)(18,21)(19,26)(20,30)(22,37)(23,33)(24,34)(25,38)(27,42)(28,43)(29,44)(31,48)(32,47)(35,41)(36,46)(39,49)(40,45)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3987);