Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23401 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3449 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1954 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)(12,13)(14,15)(16,17)(18,26)(19,23)(20,32)(21,25)(22,28)(24,35)(27,43)(29,41)(30,39)(31,42)(33,37)(34,40)(36,46)(38,45)(44,47);(16,18,21,29)(17,22,25,37)(19,27,30,44)(20,33,35,28)(23,38,39,36)(24,41,32,26)(31,46,34,45)(40,47,42,43);(13,15)(16,19)(17,23)(18,27)(20,34)(21,30)(22,36)(24,42)(25,39)(26,43)(28,46)(29,44)(31,35)(32,40)(33,45)(37,38)(41,47);(19,30)(23,39)(27,44)(31,34)(36,38)(40,42)(43,47)(45,46)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16389);