Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61109 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61109 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
2626 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,25)(15,21)(16,24)(17,23)(18,22)(19,29)(20,30)(26,34)(27,41)(28,40)(31,39)(32,36)(33,37)(35,42)(38,43);(12,14)(13,19)(15,26)(16,32)(17,29)(18,28)(20,34)(21,38)(22,36)(23,40)(24,25)(27,30)(31,42)(33,43)(35,37)(39,41);(12,15)(13,20)(14,26)(16,30)(17,33)(18,31)(19,34)(21,23)(22,37)(24,39)(25,41)(27,32)(28,42)(29,43)(35,36)(38,40);(12,15)(13,21)(14,27)(16,33)(17,30)(18,31)(19,35)(20,23)(22,39)(24,37)(25,41)(26,32)(28,43)(29,42)(34,36)(38,40);(13,22)(14,28)(20,37)(21,39)(23,24)(26,42)(27,43)(29,32)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54097);