Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61054 |
| 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 | |
2710 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)(18,27)(19,24)(20,25)(21,34)(22,26)(23,28)(29,44)(30,37)(31,40)(32,47)(33,42)(35,39)(36,43)(38,45)(41,46);(16,18,22,30)(17,23,26,39)(19,28,21,35)(20,32,33,45)(24,37,34,27)(25,41,42,44)(29,36,46,31)(38,40,47,43);(13,15)(16,19,22,21)(17,24,26,34)(18,28,30,35)(20,31,33,36)(23,37,39,27)(25,40,42,43)(29,45,46,32)(38,41,47,44);(16,20,22,33)(17,25,26,42)(18,29,30,46)(19,31,21,36)(23,38,39,47)(24,40,34,43)(27,44,37,41)(28,45,35,32);(17,26)(23,39)(24,34)(25,42)(27,37)(38,47)(40,43)(41,44)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54042);