Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23813 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×D8 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C11×#376 ◁ G | |
1022 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)(16,17,19,20)(18,21,22,23)(24,25,29,31,28,33,27,32)(26,34,37,30,35,39,36,38);(12,13)(14,15)(17,20)(21,23)(24,26,28,35)(25,30,33,38)(27,37,29,36)(31,34,32,39);(13,15)(25,31)(27,29)(30,34)(32,33)(36,37)(38,39);(16,18,19,22)(17,21,20,23)(26,35)(30,38)(34,39)(36,37)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16801);