Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23900 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#24113 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| prime radical | C7×#534 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(8,9)(10,15)(11,13)(12,14)(16,17)(18,21)(19,22)(20,23)(24,28)(25,27)(26,29)(30,31);(8,10,12,11)(9,13,14,15)(16,18)(17,21)(19,24)(20,25)(22,28)(23,27)(26,30)(29,31);(8,11,12,10)(9,13,14,15)(21,27)(28,31);(9,14)(13,15)(16,19,20,26)(17,22,23,29)(18,24,25,30)(21,28,27,31)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17101);