Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#2833 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C7 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
332 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(9,12)(13,15)(16,17,20,21)(18,22,23,19)(25,29)(30,32)(31,35)(38,39);(10,14)(13,15)(18,23)(19,22)(24,25,28,29)(26,32,34,30)(27,35,37,31)(33,38,36,39);(8,9)(10,13)(11,12)(14,15)(16,18)(17,19)(20,23)(21,22)(24,26,28,34)(25,30,29,32)(27,36,37,33)(31,39,35,38);(8,10)(9,13)(11,14)(12,15)(16,19)(17,18)(20,22)(21,23)(24,27,28,37)(25,31,29,35)(26,33,34,36)(30,38,32,39)182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16908);