Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61512 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3524 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#529 ◁ G | |
1760 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)(15,18)(19,21)(22,23)(24,32)(25,36)(26,30)(27,40)(28,34)(29,38)(31,39)(33,48)(35,43)(37,45)(41,44)(42,52)(46,50)(47,51)(49,53);(14,15)(16,19)(17,18)(20,21)(22,24)(23,28)(25,33)(26,34)(27,35)(29,42)(30,32)(31,43)(36,53)(37,49)(38,50)(39,51)(40,47)(41,52)(44,46)(45,48);(22,25,26,37)(23,29,30,44)(24,33,34,49)(27,41,39,38)(28,42,32,46)(31,45,40,36)(35,52,51,50)(43,48,47,53);(15,18)(19,21)(23,30)(24,34)(29,44)(31,40)(33,49)(35,51)(36,45)(50,52);(14,16,17,20)(15,19,18,21)(24,34)(28,32)(33,49)(35,51)(42,46)(43,47)(48,53)(50,52)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54500);