Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23990 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23990 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1260 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3,4,5,6,7)(11,18)(13,19)(14,21)(17,22);(9,13,15,19)(14,20,21,23);(8,9)(10,14)(11,19)(12,15)(13,18)(16,21)(17,23)(20,22);(8,10)(9,14)(11,17)(12,16)(13,20)(15,21)(18,22)(19,23)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16978);