Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60750 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27×C4 |
| direct product | C7×#60799 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C42×C7 ◁ G | |
2262 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,13)(12,15)(16,17)(18,25)(19,23)(20,22)(21,26)(24,28)(27,29)(30,31);(8,10,11,15)(9,12,13,14)(16,18)(17,21)(19,26)(20,27)(22,30)(23,25)(24,29)(28,31);(10,15)(12,14)(17,22)(18,26)(20,28)(21,29)(23,24)(25,30);(9,13)(12,14)(17,23)(21,25)(22,24)(29,30);(17,23)(21,25)(22,24)(29,30)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53787);