Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#2354 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C24 |
| commutator | C22 | C23×C4×C7 |
| Frattini, cosocle | C23 | C24×C7 |
| prime radical | C22×C7×D4 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
632 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3,4,5,6,7)(8,9,11,10)(12,13,14,15)(17,18)(21,22);(9,10)(16,17,20,18)(19,22,23,21);(16,18,20,17)(19,22,23,21);(8,10,11,9)(16,19,20,23)(17,21,18,22)350 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16429);