Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#22869 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C4×C7×C22⋊C4 ◁ G | |
1058 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)(10,11)(12,13,15,14)(17,22)(18,20)(23,30)(24,29)(25,27)(26,31);(12,14,15,13)(16,17,21,24)(18,22,20,29)(19,26,28,30)(23,27,31,25);(9,11)(16,18,21,20)(17,22,24,29)(19,27,28,25)(23,26,31,30);(16,19,21,28)(17,23,24,31)(18,25,20,27)(22,30,29,26)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 15857);