Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#3538 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| prime radical | C7×#525 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
1014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(16,17,21,23)(18,24,26,19)(20,28,29,22)(25,27,31,30);(9,12)(13,15)(16,18,21,26)(17,19,23,24)(20,25,29,31)(22,27,28,30);(8,9)(10,13)(11,12)(14,15);(8,10)(9,13)(11,14)(12,15)(16,19)(17,18)(20,27)(21,24)(22,25)(23,26)(28,31)(29,30);(16,20,21,29)(17,22,23,28)(18,25,26,31)(19,27,24,30)266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19256);