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×#61081 |
| 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×#532 ◁ G | |
2658 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1408 |
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)(22,28)(25,36)(27,44)(29,42)(30,47)(31,43)(32,40)(34,38)(35,41)(37,46)(39,45);(16,18,21,29)(17,22,24,38)(19,30,32,46)(20,34,36,28)(23,39,40,44)(25,42,33,26)(27,35,45,31)(37,43,47,41);(13,15)(16,17)(18,22)(19,23)(20,25)(21,24)(26,28)(27,37)(29,38)(30,39)(31,41)(32,40)(33,36)(34,42)(35,43)(44,46)(45,47);(16,19,21,32)(17,23,24,40)(18,27,29,45)(20,35,36,31)(22,37,38,47)(25,43,33,41)(26,44,42,39)(28,46,34,30);(17,24)(22,38)(23,40)(25,33)(26,42)(37,47)(39,44)(41,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54069);