Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24390 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#24762 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G | |
1060 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(9,10)(16,17,19,23,20,24,27,22)(18,21,26,30,25,29,31,28);(8,9,11,10)(12,13)(14,15)(16,18)(17,21)(19,26)(20,25)(22,28)(23,30)(24,29)(27,31);(13,15)(17,22)(19,27)(21,28)(23,24)(26,31)(29,30);(8,10,11,9)(18,25)(21,29)(26,31)(28,30)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17750);