Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2008 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23412 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #392 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C2×#392 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
1948 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)(14,24)(15,29)(16,21)(17,22)(18,23)(19,27)(20,30)(25,33)(26,34)(28,38)(31,37)(32,36)(35,41)(39,40)(42,43);(12,14)(13,19)(15,25)(16,26)(17,27)(18,28)(20,35)(21,24)(22,38)(23,34)(29,39)(30,40)(31,42)(32,41)(33,37)(36,43);(12,15)(13,20)(14,25)(16,30)(17,31)(18,32)(19,33)(21,36)(22,29)(23,37)(24,39)(26,40)(27,42)(28,41)(34,35)(38,43);(12,16,18,17)(13,21,23,22)(14,26,28,27)(15,30,32,31)(19,24,34,38)(20,36,37,29)(25,40,41,42)(33,39,35,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16400);