Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60457 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27×C4 |
| direct product | C13×#60623 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G | |
2042 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19)(17,18)(20,21)(22,23,28,30)(24,31,25,27)(26,29,34,36)(32,37,33,35);(15,18)(19,21)(22,24,27,23,28,25,31,30)(26,32,35,29,34,33,37,36);(14,16,17,20)(15,19,18,21)(22,25,27,30,28,24,31,23)(26,33,35,36,34,32,37,29);(22,26)(23,29)(24,32)(25,33)(27,35)(28,34)(30,36)(31,37);(26,34)(29,36)(32,33)(35,37)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53611);