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×#25948 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| prime radical | C22×C7×D4 | C23 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1082 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)(8,9,12,15)(10,14,11,13)(16,17,20,23)(18,21,25,29)(19,22,27,30)(24,31,26,28);(8,10,12,11)(9,13,15,14)(16,18)(17,21)(19,26)(20,25)(22,28)(23,29)(24,27)(30,31);(8,10,12,11)(9,14,15,13)(16,19)(17,22)(18,24,25,26)(20,27)(21,28,29,31)(23,30);(8,11,12,10)(9,14,15,13)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18936);