Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60460 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28×C4 |
| direct product | C11×#60651 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G | |
3138 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,21,25)(18,26,27,39)(19,23,30,37)(20,32,33,24)(22,34,35,29)(28,40,41,47)(31,44,43,38)(36,45,46,42);(16,18,20,29,21,27,33,34)(17,22,24,26,25,35,32,39)(19,28,31,42,30,41,43,45)(23,36,38,40,37,46,44,47);(12,13,14,15)(18,27)(22,35)(26,39)(28,41)(29,34)(36,46)(40,47)(42,45);(16,19)(17,23)(18,28)(20,31)(21,30)(22,36)(24,38)(25,37)(26,40)(27,41)(29,42)(32,44)(33,43)(34,45)(35,46)(39,47);(19,30)(23,37)(28,41)(31,43)(36,46)(38,44)(40,47)(42,45)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53639);