Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61609 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#62044 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#3546 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#529 ◁ G | |
1830 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(16,17,19,22)(18,24,25,31)(20,28,27,23)(21,29,30,26);(8,9)(10,13)(11,12)(14,15)(16,17)(18,21)(19,22)(20,23)(24,26)(25,30)(27,28)(29,31);(16,18,19,25)(17,21,22,30)(20,29,27,26)(23,31,28,24);(9,12)(13,15)(17,22)(21,30)(23,28)(24,31);(8,10,11,14)(9,13,12,15)(17,22)(21,30)(23,28)(24,31)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55032);