Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60457 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#60666 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C2×C13×#41 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G | |
1762 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,19)(16,20,21,18)(22,23,26,28)(24,32,34,45)(25,30,36,41)(27,39,38,31)(29,42,40,35)(33,46,47,53)(37,50,49,44)(43,52,51,48);(14,16,17,21)(15,18,19,20)(23,28)(29,40)(30,41)(31,39)(32,45)(43,51)(44,50)(46,53);(22,24,27,35,26,34,38,42)(23,29,31,32,28,40,39,45)(25,33,37,48,36,47,49,52)(30,43,44,46,41,51,50,53);(22,25)(23,30)(24,33)(26,36)(27,37)(28,41)(29,43)(31,44)(32,46)(34,47)(35,48)(38,49)(39,50)(40,51)(42,52)(45,53);(25,36)(30,41)(33,47)(37,49)(43,51)(44,50)(46,53)(48,52)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53654);