Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#34918 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| socle | C23×C7 | C25 |
| prime radical | C2×C7×#127 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
1992 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,12,13)(10,14,11,15)(16,17,19,20)(18,22,23,21)(24,25,28,29)(26,31,27,30);(9,13)(14,15)(17,20)(21,22)(25,29)(26,27);(8,10,12,11)(9,14,13,15)(16,18,19,23)(17,21,20,22)(24,26,28,27)(25,30,29,31);(24,27,28,26)(25,30,29,31);(8,11,12,10)(9,15,13,14)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 27906);