Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#25889 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#548 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C4×C7×D4 ◁ G | |
1292 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(9,11)(12,13)(14,18)(15,17)(16,19)(20,21)(22,28)(23,34)(24,29)(25,31)(26,30)(27,32)(33,35);(12,14,16,15)(13,17,19,18)(20,22,24,32)(21,27,29,28)(23,26,33,25)(30,34,31,35);(8,9,10,11)(12,14,16,15)(13,18,19,17)(20,23,26,32,24,33,25,22)(21,28,31,35,29,27,30,34);(12,15,16,14)(13,18,19,17)(21,29)(27,28)(30,31)(34,35)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18877);