Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18866 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18913 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3497 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
1122 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)(8,9,12,15)(10,14,11,13)(18,25)(19,20)(22,29)(23,27)(26,28)(30,31);(9,13)(10,11)(14,15)(16,17)(18,22)(19,23)(20,27)(21,24)(25,30)(26,31)(28,29);(16,18,21,26)(17,22,24,31)(19,25,20,28)(23,30,27,29);(8,10,12,11)(9,13,15,14)(16,19,21,20)(17,23,24,27)(18,25,26,28)(22,30,31,29)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11901);