Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24429 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#2416 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G | |
1508 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(21,25)(22,26)(23,27);(16,17)(18,19)(20,21,24,22)(23,26,27,25);(13,15)(17,19);(20,22,24,21)(23,25,27,26)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17417);