Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#3568 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
958 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,13,15)(10,19,23,21)(11,14,18,24)(12,26,27,17)(16,30,29,20)(22,35,36,33)(25,37,32,28)(31,34,38,39);(9,15)(10,20)(11,18)(16,21)(17,26)(19,29)(22,34)(23,30)(25,32)(31,35)(33,38)(36,39);(8,10,13,23)(9,16,15,29)(11,21,18,19)(12,22,27,36)(14,20,24,30)(17,31,26,38)(25,35,32,33)(28,34,37,39);(8,11,24,9)(10,21,30,16)(12,25,37,17)(13,18,14,15)(19,20,29,23)(22,35,39,31)(26,27,32,28)(33,34,38,36);(8,12,24,37)(9,17,11,25)(10,22,30,39)(13,27,14,28)(15,26,18,32)(16,31,21,35)(19,33,29,38)(20,34,23,36)266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19286);