Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61073 |
| 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 | |
2706 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)(22,30)(25,34)(27,40)(28,37)(29,36)(31,44)(32,38)(35,43)(39,45)(41,47)(42,46);(16,18)(17,22)(19,27)(20,28)(21,29)(23,35)(24,37)(25,36)(26,33)(30,34)(31,41)(32,42)(38,47)(39,46)(40,44)(43,45);(13,15)(16,19,21,32)(17,23,24,38)(18,27,29,42)(20,31,34,45)(22,35,37,47)(25,39,33,44)(26,40,36,46)(28,41,30,43);(18,28)(20,34)(22,36)(25,33)(26,37)(27,41)(29,30)(31,45)(35,46)(39,44)(40,47)(42,43);(17,24)(18,29)(23,38)(25,33)(27,42)(28,30)(39,44)(41,43)605 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54061);