Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3198 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#22275 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#127 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C11×#376 ◁ G | |
938 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)(12,13,15,14)(16,17)(18,21)(19,22)(20,23)(24,25)(26,28)(27,34)(29,33)(30,37)(31,35)(32,38)(36,39);(12,14,15,13)(16,18,21,17)(19,22,20,23)(24,26,28,25)(27,30,36,32)(29,33,35,31)(34,38,39,37);(16,19,21,20)(17,22,18,23)(24,27,35,38,28,36,29,37)(25,30,33,39,26,32,31,34);(16,20,21,19)(17,22,18,23)(25,26)(30,32)(31,33)(34,39)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15263);