Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#33583 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
702 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,22,27)(18,28,31,45)(19,26,21,24)(20,33,36,41)(23,38,40,30)(25,32,43,35)(29,46,37,42)(34,44,47,39);(12,13,14,15);(16,18)(17,23)(19,29)(20,34)(21,37)(22,31)(24,39)(25,42)(26,44)(27,40)(28,33)(30,35)(32,38)(36,47)(41,45)(43,46);(16,19,22,21)(17,24,27,26)(18,29,31,37)(20,32,36,35)(23,39,40,44)(25,41,43,33)(28,42,45,46)(30,34,38,47)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26571);