Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62892 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C7×#62894 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
7294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 6 generators on 31 points:
(1,2,3,4,5,6,7)(9,12)(13,15)(16,17,21,24)(18,19,26,22)(20,28,29,23)(25,30,31,27);(16,17)(18,19)(20,23)(21,24)(22,26)(25,27)(28,29)(30,31);(8,9)(10,13)(11,12)(14,15)(16,18)(17,22)(19,24)(20,25)(21,26)(23,30)(27,28)(29,31);(10,14)(13,15)(16,19,21,22)(17,18,24,26)(20,27,29,30)(23,25,28,31);(8,10)(9,13)(11,14)(12,15)(16,18)(17,19)(20,25)(21,26)(22,24)(23,27)(28,30)(29,31);(8,9)(10,13)(11,12)(14,15)(16,20)(17,23)(18,25)(19,27)(21,29)(22,30)(24,28)(26,31)511 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55882);