Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#36701 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| socle, prime radical | C23×C13 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
1304 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 3328 |
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)(16,19)(17,18)(20,21)(22,23)(24,28)(25,29)(26,27)(30,36)(31,34)(32,37)(33,35)(38,39,42,45)(40,43,47,51)(41,44,49,53)(46,50,48,52);(23,27)(28,34)(29,35)(36,37)(38,40,42,47)(39,43,45,51)(41,48,49,46)(44,52,53,50);(15,18)(19,21)(22,24,26,31)(23,28,27,34)(25,32,33,30)(29,37,35,36)(38,41)(39,44)(40,46)(42,49)(43,50)(45,53)(47,48)(51,52);(22,25,26,33)(23,29,27,35)(24,30,31,32)(28,36,34,37)(39,45)(41,49)(43,51)(46,48);(14,16,17,20)(15,19,18,21)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 29689);