Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#3444 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C7 | C23 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| socle | C22×C7 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42×C7 ◁ G | |
1212 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 5 generators on 23 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17)(18,21)(19,20)(22,23);(9,12)(13,15);(17,20)(21,23);(16,18,19,22)(17,21,20,23);(8,10,11,14)(9,13,12,15)392 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19162);