Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61061 |
| 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 ◁ C11×#525 ◁ G | |
2674 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)(12,13)(14,15)(16,17)(18,26)(19,23)(20,33)(21,24)(22,29)(25,36)(27,42)(28,44)(30,47)(31,43)(32,40)(34,37)(35,41)(38,46)(39,45);(16,18,21,27)(17,22,24,37)(19,30,32,46)(20,34,36,29)(23,39,40,44)(25,42,33,26)(28,35,45,31)(38,43,47,41);(13,15)(18,27)(22,37)(26,42)(28,45)(29,34)(30,46)(38,47)(39,44);(16,19,21,32)(17,23,24,40)(18,28,27,45)(20,35,36,31)(22,38,37,47)(25,43,33,41)(26,44,42,39)(29,46,34,30);(17,24)(22,37)(23,40)(25,33)(26,42)(38,47)(39,44)(41,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54049);