Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23860 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#24739 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#127 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C4×C7×C4⋊C4 ◁ G | |
990 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)(12,13,14,15)(16,17)(18,25)(19,29)(20,24)(21,23)(22,28)(26,31)(27,30);(8,9,11,10)(16,18)(17,22)(19,27)(20,28)(21,26)(23,30)(24,25)(29,31);(13,15)(18,26)(19,21)(22,30)(23,29)(25,31)(27,28);(8,10,11,9)(16,19,20,21)(17,23,24,29)(18,27,28,26)(22,30,25,31)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17727);