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×#3500 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
1540 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)(14,20)(15,23)(16,17)(18,22)(19,24)(21,25)(26,27);(13,17)(18,20)(19,23)(25,26);(8,9,10,11)(12,14)(13,18)(15,21)(16,22)(17,20)(19,25)(23,26)(24,27);(12,13)(14,18)(15,19)(16,17)(20,22)(21,25)(23,24)(26,27);(12,15,16,24)(13,19,17,23)(14,21,22,27)(18,25,20,26)308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19218);