Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #15257 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25×C4 |
| direct product | C7×#15909 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C7 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| prime radical | C2×C7×#392 | C2 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
2150 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(9,11)(13,15)(18,22)(21,23)(25,26)(27,31);(17,20)(21,23)(24,25,28,26)(27,30,31,29);(12,13)(14,15)(16,17)(18,21)(19,20)(22,23)(24,26,28,25)(27,30,31,29);(8,9)(10,11)(12,13)(14,15)(16,18,19,22)(17,21,20,23)(24,27,28,31)(25,29,26,30)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 8897);