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×#23641 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G | |
1014 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)(18,21)(19,20)(22,23)(24,25,28,33,29,34,27,32)(26,30,35,38,36,39,37,31);(12,13)(14,15)(17,20)(21,23)(24,26)(25,30)(27,37)(28,35)(29,36)(31,32)(33,38)(34,39);(13,15)(16,18,19,22)(17,21,20,23)(24,26)(25,31)(27,35)(28,37)(29,36)(30,32)(33,39)(34,38);(24,27,29,28)(25,32,34,33)(26,35,36,37)(30,38,39,31)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16629);