Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#1840 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C23 |
| commutator | C23 | C22×C4×C7 |
| Frattini, cosocle | C22×C4 | C23×C7 |
| socle, prime radical | C23×C7 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
196 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,15)(11,13)(12,14)(16,17)(18,20)(19,21)(22,23)(24,25,27,30,28,31,34,37)(26,29,33,36,32,35,38,39);(8,10,12,11)(9,13,14,15)(16,18,19,22)(17,20,21,23)(24,26)(25,29)(27,33)(28,32)(30,36)(31,35)(34,38)(37,39);(8,11,12,10)(9,13,14,15)(17,21)(20,23)(26,32)(29,35)(33,38)(36,39)308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5075);