Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27×C4 |
| direct product | C13×#60826 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G | |
2026 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
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)(16,20)(17,19)(18,21)(22,23,27,32)(24,28,33,41)(25,30,36,44)(26,29,38,31)(34,40,46,51)(35,42,47,39)(37,43,49,45)(48,52,53,50);(14,16,17,21)(15,18,19,20)(22,24)(23,28)(25,34)(26,35)(27,33)(29,42)(30,40)(31,39)(32,41)(36,46)(37,48)(38,47)(43,52)(44,51)(45,50)(49,53);(16,21)(18,20)(23,29)(24,33)(26,38)(28,39)(30,43)(31,32)(34,46)(37,49)(40,50)(41,42)(44,45)(51,52);(15,19)(18,20)(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);(25,36)(30,44)(34,46)(37,49)(40,51)(43,45)(48,53)(50,52)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53814);