Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18618 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18646 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
1024 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)(9,13)(10,11)(14,15)(16,17)(18,26)(19,22)(20,24)(21,25)(23,27)(28,31)(29,30);(8,9,12,15)(10,13,11,14)(17,22)(19,20)(23,30)(24,25)(26,31)(27,28);(8,10,12,11)(9,13,15,14)(16,18,21,29)(17,23,25,31)(19,27,20,28)(22,30,24,26);(8,10,12,11)(9,14,15,13)(16,19,21,20)(17,24,25,22)(18,27,29,28)(23,26,31,30)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11634);