Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4×#120 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28×C4 |
| direct product | C11×#36592 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
4122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 27 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(17,18)(20,21,24,22)(23,25,27,26);(16,17,19,18)(20,21,24,22)(23,26,27,25);(12,13,14,15)(16,18,19,17)(21,22)(25,26);(20,22,24,21)(23,25,27,26);(20,23,24,27)(21,25,22,26)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29580);