Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18746 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18787 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×D4×#41 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
1206 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,11,14)(10,12,15,13)(16,17,21,26)(18,27,30,31)(19,25,20,24)(22,28,23,29);(9,12)(10,15)(13,14)(16,18)(17,22)(19,28)(20,29)(21,30)(23,26)(24,31)(25,27);(16,18)(17,23)(19,28)(20,29)(21,30)(22,26)(24,27)(25,31);(16,19,21,20)(17,24,26,25)(18,28,30,29)(22,31,23,27)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11775);