Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#11303 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | #121 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| prime radical | C24×C7 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C23×C4×C7 ◁ G | |
590 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,10,11)(12,13,15,14)(16,17)(18,26)(19,22)(20,24)(21,25)(23,29)(27,30)(28,31);(12,14,15,13)(17,22)(18,27)(19,20)(23,26)(24,25)(30,31);(13,14)(16,18,19,28,21,27,20,29)(17,23,24,30,25,31,22,26)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 4291);