Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62851 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
7066 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)(24,27)(25,26)(28,36)(29,31)(30,37)(32,33)(34,35);(14,15,17,18)(16,19,20,21)(22,24,29,26)(23,25,31,27)(28,32,37,34)(30,33,36,35);(22,25,29,27)(23,24,31,26)(28,33,37,35)(30,32,36,34);(22,26,29,24)(23,25,31,27)(28,34,37,32)(30,33,36,35);(14,16,17,20)(15,19,18,21)(22,27,29,25)(23,24,31,26)(28,35,37,33)(30,32,36,34);(22,28)(23,30)(24,32)(25,33)(26,34)(27,35)(29,37)(31,36)1066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55839);