Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C8 |
| direct product | C11×#8270 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C11 | C2×D4 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | C4×C4⋊C4 |
| prime radical | C23×C11 | #117 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
342 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17,19,22)(18,24,25,26)(28,29)(30,33)(31,35)(32,34)(36,40)(37,39)(38,41)(42,43);(12,13)(14,18)(15,22)(16,19)(17,23)(20,26)(21,25)(24,27)(28,30,31,36,32,37,38,42)(29,33,35,40,34,39,41,43);(12,14,15,20,16,21,23,27)(13,18,22,26,19,25,17,24)(29,34)(33,39)(35,41)(40,43)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1258);