Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#33589 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
726 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
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)(18,23)(19,25)(20,33)(21,37)(22,27)(24,29)(26,35)(28,38)(30,41)(31,40)(32,44)(34,39)(36,47)(42,46)(43,45);(12,13,14,15)(16,18)(17,23)(19,31)(20,29)(21,28)(22,30)(24,33)(25,40)(26,39)(27,41)(32,46)(34,35)(36,45)(37,38)(42,44)(43,47);(16,18)(17,24)(19,28)(20,34)(21,31)(22,30)(23,33)(25,39)(26,40)(27,43)(29,35)(32,45)(36,46)(37,42)(38,44)(41,47);(16,19,22,21)(17,25,27,37)(18,28,30,31)(20,32,36,35)(23,38,41,40)(24,39,43,42)(26,33,44,47)(29,34,45,46)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26577);