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×#33587 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#3155 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
712 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)(18,26)(19,29)(20,31)(22,34)(24,39)(25,38)(27,44)(28,43)(30,33)(32,42)(35,46)(36,47)(37,45)(40,41);(12,13,14,15)(16,17)(18,22)(19,24)(20,25)(21,23)(26,34)(27,36)(28,35)(29,39)(30,40)(31,38)(32,37)(33,41)(42,45)(43,46)(44,47);(16,18,21,28)(17,22,23,35)(19,30,32,44)(20,33,31,27)(24,40,37,47)(25,41,38,36)(26,42,43,29)(34,45,46,39);(17,23)(22,35)(24,37)(25,38)(34,46)(36,41)(39,45)(40,47)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26575);