Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28×C4 |
| direct product | C7×#34641 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| socle | C23×C7 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
3694 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7)(9,11)(13,15)(16,17)(18,21)(19,23)(20,22)(24,27)(25,28)(26,29)(30,31);(8,9,10,11)(16,18)(17,21)(19,25)(20,24)(22,27)(23,28)(26,30)(29,31);(12,13,14,15)(18,24)(21,27)(25,30)(28,31);(17,22)(21,27)(23,29)(28,31);(16,19,20,26)(17,23,22,29)(18,25,24,30)(21,28,27,31)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 27629);