Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #34980 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#34988 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
4082 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(18,22)(21,23)(24,25)(26,31)(27,28)(29,30);(17,20)(21,23)(25,30)(26,27);(12,13)(14,15)(16,17)(18,21)(19,20)(22,23)(24,26,29,27)(25,31,30,28);(16,17)(18,21)(19,20)(22,23)(24,27,29,26)(25,28,30,31);(16,18)(17,21)(19,22)(20,23)(24,28)(25,26)(27,30)(29,31)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27976);