Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24404 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#25949 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| prime radical | C2×C7×#120 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1202 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,12,15)(10,14,11,13)(16,17,20,23)(18,24,26,21)(19,22,28,30)(25,29,27,31);(8,10,12,11)(9,13,15,14)(16,18,20,26)(17,21,23,24)(19,27,28,25)(22,29,30,31);(8,10,12,11)(9,14,15,13)(16,19,20,28)(17,22,23,30)(18,25)(21,29)(24,31)(26,27);(8,11,12,10)(9,14,15,13)(17,23)(21,24)(22,30)(29,31)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18937);