Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C29 |
| direct product | C7×#3489 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
1522 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 5 generators on 27 points:
(1,2,3,4,5,6,7)(9,11)(12,13,17,18)(14,20,22,15)(16,24,25,19)(21,23,27,26);(13,18)(15,20)(19,24)(23,26);(8,9)(10,11)(12,14)(13,15)(16,21)(17,22)(18,20)(19,23)(24,26)(25,27);(12,15)(13,14)(16,23)(17,20)(18,22)(19,21)(24,27)(25,26);(12,16,17,25)(13,19,18,24)(14,21,22,27)(15,23,20,26)308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19207);