Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62833 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
7050 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)(23,28)(24,32)(25,35)(31,36);(16,20)(19,21)(22,23,27,28)(24,33,32,29)(25,30,35,37)(26,36,34,31);(14,15)(16,19)(17,18)(20,21)(22,24,27,32)(23,29,28,33)(25,34,35,26)(30,36,37,31);(22,25)(23,30)(24,34)(26,32)(27,35)(28,37)(29,36)(31,33);(14,16,17,20)(15,19,18,21)(22,26,27,34)(23,31,28,36)(24,25,32,35)(29,30,33,37);(14,15)(16,19)(17,18)(20,21)(22,25)(23,30)(24,34)(26,32)(27,35)(28,37)(29,36)(31,33)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55821);