Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24278 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24280 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1328 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)(16,17)(18,26)(19,33)(20,37)(21,28)(22,27)(23,29)(24,31)(25,35)(30,44)(32,40)(34,47)(36,43)(38,42)(39,46)(41,45);(12,13)(14,15)(16,18,21,31,23,32,22,20)(17,24,27,26,29,37,28,40)(19,30,35,45,36,46,38,34)(25,39,33,41,42,44,43,47);(13,15)(16,19)(17,25)(18,30)(20,34)(21,35)(22,38)(23,36)(24,39)(26,41)(27,33)(28,43)(29,42)(31,45)(32,46)(37,44)(40,47);(16,20,22,32,23,31,21,18)(17,26,28,24,29,40,27,37)(19,34,38,46,36,45,35,30)(25,41,43,39,42,47,33,44)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17268);