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×#7451 |
| 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)(22,23,25,31,41,50,53,29,28,34,24,35,27,33,42,47,26,32,39,46,37,48,36,45,44,51,38,30,43,49,40,52);(14,15,17,19)(16,21,20,18)(23,29)(24,36)(25,40)(27,37)(28,44)(30,33)(31,50)(32,45)(34,52)(35,49)(38,53)(39,42)(41,43)(46,48)(47,51)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 439);