Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#8936 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | #385 |
| prime radical | C23×C11 | #123 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G | |
356 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17)(15,22)(18,26)(19,23)(20,24)(25,27)(28,29,32,36,33,31,40,35)(30,34,38,42,39,37,43,41);(12,13)(14,18)(15,23)(16,19)(17,22)(20,25)(21,27)(24,26)(28,30,32,38,33,39,40,43)(29,34,36,42,31,37,35,41);(12,14,16,21)(13,18,19,27)(15,24,22,20)(17,25,23,26)(28,31)(29,33)(30,37)(32,35)(34,39)(36,40)(38,41)(42,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1924);