Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60388 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C210 |
| direct product | C11×#60390 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C22×#120 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C11×#41 ◁ G | |
4698 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)(13,18)(16,27)(19,32)(20,31)(21,28)(23,29)(26,38)(30,34)(33,42)(35,39)(37,40)(41,43);(12,13)(14,19)(15,20)(16,28)(17,21)(18,27)(22,33)(23,30)(24,34)(25,35)(26,39)(29,32)(31,38)(36,43)(37,41)(40,42);(12,14,17,24)(13,19,21,34)(15,22,25,36)(16,29,27,23)(18,30,28,32)(20,33,35,43)(26,40,38,37)(31,41,39,42);(12,15)(13,20)(14,22)(16,26)(17,25)(18,31)(19,33)(21,35)(23,37)(24,36)(27,38)(28,39)(29,40)(30,41)(32,42)(34,43);(15,25)(20,35)(22,36)(26,38)(31,39)(33,43)(37,40)(41,42)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53378);