Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60756 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60930 |
| 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 | |
1804 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(16,17)(18,21)(19,27)(20,25)(22,24)(23,28)(26,30)(29,31);(8,9)(10,13)(11,12)(14,15)(16,18,21,17)(19,23,29,26)(20,25,22,24)(27,30,31,28);(9,12)(13,15)(16,19)(17,23)(18,26)(20,28)(21,29)(22,30)(24,27)(25,31);(8,10,11,14)(9,13,12,15)(16,20,21,22)(17,24,18,25)(19,28,29,30)(23,27,26,31);(16,20,21,22)(17,25,18,24)(19,28,29,30)(23,31,26,27)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53918);