Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#2842 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C7 |
| prime radical | C25×C7 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
548 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(9,12)(13,15)(16,17)(18,20)(19,21)(22,23)(26,30)(28,31);(10,14)(13,15)(17,18)(21,22)(24,25,27,29)(26,31,30,28);(8,9)(10,13)(11,12)(14,15)(16,18,20,17)(19,21,23,22)(24,26,27,30)(25,28,29,31);(8,10)(9,13)(11,14)(12,15)(16,19)(17,21)(18,22)(20,23)(24,25)(26,28)(27,29)(30,31)182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16917);