Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #34980 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C29 |
| direct product | C7×#35089 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C2×C7×#534 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
3238 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7)(9,11)(13,15)(19,26)(23,28)(25,30)(29,31);(12,13,14,15)(17,21)(18,24)(23,28)(25,30);(8,9)(10,11)(16,17,20,21)(18,22,24,27)(19,23,26,28)(25,29,30,31);(16,18)(17,22)(19,25)(20,24)(21,27)(23,29)(26,30)(28,31);(16,19)(17,23)(18,25)(20,26)(21,28)(22,29)(24,30)(27,31)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 28077);