Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#24093 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#555 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G | |
1116 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17)(18,23)(19,21)(20,22)(25,30)(26,34)(27,29)(31,35)(36,37)(38,39);(16,18,20,19)(17,21,22,23)(24,25)(26,35)(27,32)(28,30)(29,33)(31,36)(34,38)(37,39);(13,15)(16,19,20,18)(17,21,22,23)(24,26,28,37)(25,31,30,38)(27,36,29,34)(32,39,33,35);(17,22)(21,23)(24,27,28,29)(25,32,30,33)(26,36,37,34)(31,39,38,35)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17081);