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) = C24 |
| direct product | C11×#8987 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | #120 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
576 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,18,21,19,22,23,20)(24,25)(26,32,34,39)(27,29)(28,31)(30,33,37,36)(35,38);(12,13,14,15)(17,20)(18,23)(21,22)(25,29)(28,35)(30,37)(33,36);(24,26,27,34)(25,30,29,37)(28,36,35,33)(31,39,38,32)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1975);