Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#2775 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C7 |
| prime radical | C24×C7 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
386 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,12,10)(11,14,15,13)(16,17)(18,21)(19,20)(22,23)(25,28)(29,30);(9,10)(11,15)(17,19)(21,22)(24,25,27,28)(26,30,31,29);(8,10,12,9)(11,14,15,13)(16,18,20,23)(17,21,19,22)(24,25)(26,29)(27,28)(30,31);(8,11,12,15)(9,13,10,14)(16,19,20,17)(18,22,23,21)(24,26,27,31)(25,29,28,30)224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16850);