Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#2783 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C7 |
| prime radical | C24×C7 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
378 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(16,17,19,21)(18,22,23,20)(25,26)(29,30);(9,12)(13,15)(24,25,28,26)(27,30,31,29);(8,9)(10,13)(11,12)(14,15)(16,17)(18,20)(19,21)(22,23)(24,26,28,25)(27,30,31,29);(8,10,11,14)(9,13,12,15)(16,18,19,23)(17,20,21,22)(24,27)(25,29)(26,30)(28,31)224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16858);