Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61292 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#532 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#532 ◁ G | |
1746 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)(14,15,18,17)(16,20,21,19)(22,23,27,31)(24,28,33,41)(25,30,36,45)(26,29,38,32)(34,40,46,51)(35,42,47,39)(37,43,49,44)(48,52,53,50);(14,16)(15,19)(17,20)(18,21)(22,24)(23,28)(25,34)(26,35)(27,33)(29,42)(30,40)(31,41)(32,39)(36,46)(37,48)(38,47)(43,52)(44,50)(45,51)(49,53);(14,17,18,15)(16,20,21,19)(23,29)(24,33)(26,38)(28,39)(30,43)(31,32)(34,46)(37,49)(40,50)(41,42)(44,45)(51,52);(16,21)(19,20)(22,25)(23,30)(24,34)(26,37)(27,36)(28,40)(29,43)(31,45)(32,44)(33,46)(35,48)(38,49)(39,50)(41,51)(42,52)(47,53);(23,31)(24,33)(25,36)(29,32)(35,47)(37,49)(40,51)(50,52)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54280);