Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18132 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18141 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3459 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1004 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,21)(14,22,24,27)(15,20,16,19)(18,25,26,23)(28,29,32,35)(30,33,37,40)(31,34,38,41)(36,42,43,39);(12,14)(13,18)(15,23)(16,25)(17,24)(19,22)(20,27)(21,26)(28,30)(29,33)(31,36)(32,37)(34,39)(35,40)(38,43)(41,42);(28,31)(29,34)(30,36)(32,38)(33,39)(35,41)(37,43)(40,42);(12,15,17,16)(13,19,21,20)(14,23,24,25)(18,22,26,27)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11129);