Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60756 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27×C4 |
| direct product | C7×#60836 |
| 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 ◁ C4×C7×#41 ◁ G | |
2072 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)(10,14)(11,13)(12,15)(18,24)(19,26)(21,28)(23,30)(25,27)(29,31);(8,10,11,15)(9,12,13,14)(16,17)(18,21)(19,23)(20,22)(24,28)(25,29)(26,30)(27,31);(10,15)(12,14)(16,18,20,25)(17,21,22,29)(19,27,26,24)(23,31,30,28);(9,13)(12,14)(16,17)(18,21)(19,23)(20,22)(24,28)(25,29)(26,30)(27,31);(17,22)(21,29)(23,30)(28,31)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53824);