Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#21070 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C22×C13 | C2×C4×D4 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C8×C13 ◁ G | |
1026 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16)(18,19,23,28,24,27,22,36)(20,25,31,40,32,39,30,46)(21,33,34,26,35,42,37,41)(29,43,44,38,45,49,47,48);(14,15,17,16)(18,20,23,31,24,32,22,30)(19,25,28,40,27,39,36,46)(21,29,34,44,35,45,37,47)(26,38,42,49,41,48,33,43);(14,16,17,15)(18,21)(19,26)(20,29)(22,37)(23,34)(24,35)(25,38)(27,41)(28,42)(30,47)(31,44)(32,45)(33,36)(39,48)(40,49)(43,46);(19,27)(25,39)(26,41)(28,36)(33,42)(38,48)(40,46)(43,49)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 14058);