Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#34636 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| socle | C23×C11 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
2390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17)(18,21)(19,20)(22,23)(24,25)(26,29)(27,31)(28,30)(32,35)(33,36)(34,37)(38,39);(17,20)(21,23)(24,26)(25,29)(27,33)(28,32)(30,35)(31,36)(34,38)(37,39);(13,15)(26,32)(29,35)(33,38)(36,39);(16,18,19,22)(17,21,20,23)(25,30)(29,35)(31,37)(36,39);(24,27,28,34)(25,31,30,37)(26,33,32,38)(29,36,35,39)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27624);