Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×#7450 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C13 | #357 |
| commutator | C2×C16 | C2×C4×C13 |
| Frattini, cosocle | C4×C16 | C22×C13 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ C4×C8×C13 ◁ C4×C13×C16 ◁ G | |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 2 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(16,20)(19,21)(22,23,24,29,34,42,49,40,26,31,35,43,38,46,50,41,27,32,36,44,51,53,52,47,37,45,48,39,25,30,33,28);(14,15,17,19)(16,21,20,18)(23,28)(24,33)(25,34)(26,37)(29,30)(31,47)(32,41)(35,52)(36,50)(38,51)(39,42)(40,45)(43,53)(44,46)(48,49)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 438);