Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18866 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18905 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C22×D4×C11 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
926 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,21)(14,22,25,26)(15,20,16,19)(18,23,27,24)(28,29)(30,38)(31,36)(32,35)(33,37)(34,40)(39,42)(41,43);(12,14,17,25)(13,18,21,27)(15,24,16,23)(19,22,20,26)(28,30,33,39)(29,34,37,43)(31,41,32,40)(35,42,36,38);(29,35)(31,32)(34,42)(36,37)(38,43)(40,41);(12,15,17,16)(13,19,21,20)(14,23,25,24)(18,26,27,22)(30,39)(34,43)(38,42)(40,41)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11893);