Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1705 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C4 |
| direct product | C7×#1711 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #127 |
| commutator, Frattini, cosocle | C42 | C23×C7 |
| prime radical | C7×#127 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C42×C7 ◁ G | |
178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,16)(11,20)(12,14)(13,18)(15,17)(19,22)(21,23)(24,25)(26,32)(27,29)(28,36)(30,34)(31,35)(33,38)(37,39);(8,10,17,23,12,19,11,18)(9,13,20,22,14,21,15,16)(25,29)(30,37)(31,36)(32,38);(9,14)(13,21)(15,20)(16,22)(24,26,28,34,27,33,35,39)(25,30,31,32,29,37,36,38)266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4946);