Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13015 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C2×D8 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
490 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19)(20,21)(22,23,26,32,42,51,40,29,28,34,25,31,27,33,43,47)(24,35,37,53,45,50,41,49,39,46,36,48,38,52,44,30);(14,15,16,17)(23,29)(25,40)(26,43)(27,42)(30,46)(31,33)(32,51)(34,47)(35,49)(36,41)(37,44)(38,45)(48,52)(50,53);(19,21)(22,24,28,39)(23,30,34,49)(25,41,26,44)(27,45,42,38)(29,46,47,35)(31,50,32,52)(33,53,51,48)(36,43,37,40)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6003);