Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61105 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C2×C11 | C2×D42 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ G | |
2620 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)(14,24)(15,26)(16,21)(17,22)(18,35)(19,23)(20,29)(25,41)(27,30)(28,42)(31,43)(32,38)(33,39)(34,40)(36,37);(12,14)(13,15)(16,31)(17,26)(18,27)(19,20)(21,37)(22,29)(23,30)(24,35)(25,32)(28,39)(33,36)(34,42)(38,43)(40,41);(12,15)(13,20)(14,23)(16,28)(17,29)(18,24)(19,30)(21,36)(22,27)(25,40)(26,35)(31,38)(32,37)(33,41)(34,43)(39,42);(12,16)(13,21)(14,25)(15,28)(17,32)(18,33)(19,34)(20,36)(22,38)(23,40)(24,41)(26,42)(27,31)(29,37)(30,43)(35,39);(12,17,19,18)(13,22,23,35)(14,26,20,27)(15,29,30,24)(16,32,34,33)(21,38,40,39)(25,42,36,31)(28,37,43,41)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54093);