Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23924 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24070 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#540 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G | |
1130 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)(18,23)(19,21)(20,22)(24,25)(26,31)(27,36)(28,32)(29,37)(30,33)(34,38)(35,39);(12,13)(14,15)(16,18,20,19)(17,21,22,23)(24,26)(25,31)(27,28)(29,34)(30,35)(32,36)(33,39)(37,38);(13,15)(16,19,20,18)(17,21,22,23)(24,27)(25,31)(26,28)(29,35)(30,34)(32,38)(33,39)(36,37);(17,22)(21,23)(24,28,30,29)(25,32,33,37)(26,34,35,27)(31,38,39,36)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17058);