Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4×#120 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C29 |
| direct product | C7×#36576 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
3244 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 23 points:
(1,2,3,4,5,6,7)(9,11)(13,15)(16,17,20,19)(18,21,23,22);(12,13,14,15)(17,19)(21,22);(8,9)(10,11)(16,17,20,19)(18,22,23,21);(16,18,20,23)(17,21,19,22);(16,19,20,17)(18,21,23,22)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29564);