Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3192 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25×C4 |
| direct product | C11×#21840 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G | |
1238 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)(12,13,14,15)(16,17)(18,21)(19,22)(20,23)(24,25)(26,32)(27,30)(28,31)(29,34)(33,38)(35,37)(36,39);(16,18,20,19)(17,21,23,22)(24,26,28,34)(25,29,31,32)(27,35,36,33)(30,38,39,37);(17,22)(18,19)(21,23)(24,27,28,36)(25,30,31,39)(26,33,34,35)(29,37,32,38);(25,31)(29,32)(30,39)(37,38)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14828);