Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61663 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#532 ◁ G | |
2064 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)(24,29)(25,31)(26,32)(27,41)(28,33)(30,37)(34,43)(35,44)(36,46)(38,47)(39,45)(40,48)(42,50)(49,52)(51,53);(14,16)(15,18)(17,21)(19,20)(22,24,28,36)(23,29,33,46)(25,34,38,51)(26,39,27,35)(30,42,48,52)(31,43,47,53)(32,45,41,44)(37,50,40,49);(22,25)(23,30)(24,34)(26,37)(27,40)(28,38)(29,42)(31,41)(32,47)(33,48)(35,49)(36,51)(39,50)(43,44)(45,53)(46,52);(16,21)(18,20)(22,25)(23,31)(24,34)(26,40)(27,37)(28,38)(29,43)(30,41)(32,48)(33,47)(35,50)(36,51)(39,49)(42,44)(45,52)(46,53);(15,19)(18,20)(22,26,28,27)(23,32,33,41)(24,35,36,39)(25,37,38,40)(29,44,46,45)(30,47,48,31)(34,49,51,50)(42,43,52,53)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54651);