Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#61220 |
| 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 ◁ C7×#532 ◁ G | |
2082 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)(8,9,11,13)(10,14,15,12)(16,17)(18,24)(19,28)(20,22)(21,26)(23,30)(25,29)(27,31);(8,10)(9,12)(11,15)(13,14)(16,17)(18,25)(19,23)(20,22)(21,27)(24,29)(26,31)(28,30);(16,18,20,27)(17,21,22,25)(19,29,30,26)(23,31,28,24);(10,15)(12,14)(16,17)(18,21)(19,23)(20,22)(24,26)(25,27)(28,30)(29,31);(17,22)(21,25)(23,28)(24,31)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54208);