Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #14715 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#15187 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C7 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
1210 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(12,13)(14,16)(15,18)(17,19)(20,21,23,25)(22,26,27,24)(29,31)(33,34);(9,11)(13,14)(17,18)(20,21,23,25)(22,24,27,26)(28,29,32,31)(30,33,35,34);(8,9)(10,11)(12,14,16,13)(15,18,19,17)(20,21)(22,24)(23,25)(26,27)(28,30,32,35)(29,33,31,34);(12,15,16,19)(13,17,14,18)(20,22,23,27)(21,24,25,26)(28,31,32,29)(30,34,35,33)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 8175);