Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#2529 |
| 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 | |
398 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)(8,9)(10,12)(11,14)(13,15)(16,17,19,21)(18,20,22,23)(26,30)(29,31);(9,10)(13,14)(16,17,19,21)(18,20,22,23)(24,25,28,27)(26,29,30,31);(8,10,12,9)(11,14,15,13)(16,17)(18,20)(19,21)(22,23)(24,26)(25,29)(27,31)(28,30);(8,11,12,15)(9,13,10,14)(16,18,19,22)(17,20,21,23)(24,27,28,25)(26,31,30,29)266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16604);