Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18383 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×D4×C11 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,22)(14,24,28,40)(15,21,16,31)(18,23,34,41)(19,25,37,26)(20,30,32,33)(27,35,29,39)(36,42,38,43);(12,14,17,28)(13,19,22,37)(15,26,16,25)(18,29,34,27)(20,39,32,35)(21,40,31,24)(23,38,41,36)(30,42,33,43);(12,13)(14,19)(15,20)(16,32)(17,22)(18,23)(21,33)(24,42)(25,35)(26,39)(27,36)(28,37)(29,38)(30,31)(34,41)(40,43);(12,15,17,16)(13,20,22,32)(14,25,28,26)(18,30,34,33)(19,35,37,39)(21,23,31,41)(24,38,40,36)(27,42,29,43)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11371);