Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62892 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62917 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
7186 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(19,21)(22,23,29,32)(24,33,27,30)(25,28,26,31)(34,35,36,37);(22,24,29,27)(23,30,32,33)(25,36,26,34)(28,35,31,37);(14,15)(16,19)(17,18)(20,21)(22,25,29,26)(23,31,32,28)(24,34,27,36)(30,35,33,37);(16,20)(19,21)(22,26,29,25)(23,28,32,31)(24,34,27,36)(30,35,33,37);(14,16,17,20)(15,19,18,21)(22,27,29,24)(23,30,32,33)(25,36,26,34)(28,37,31,35);(14,15)(16,19)(17,18)(20,21)(22,28)(23,25)(24,35)(26,32)(27,37)(29,31)(30,36)(33,34)949 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55905);