Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11663 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#12738 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#102 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C22×C13×#135 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ C23×C8×C13 ◁ G | |
926 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)(18,19,21,25,23,28,35,27)(20,29,32,43,33,46,30,45)(22,36,34,26,38,42,47,44)(24,37,40,31,41,48,39,49);(18,20)(19,24)(21,30)(22,37)(23,33)(25,39)(26,43)(27,40)(28,41)(29,42)(31,47)(32,35)(34,49)(36,46)(38,48)(44,45);(15,17)(18,21,23,35)(19,25,28,27)(20,30,33,32)(22,34,38,47)(24,39,41,40)(26,42,44,36)(29,45,46,43)(31,37,49,48)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5726);