Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#17876 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C42 | C24×C7 |
| socle | C22×C7 | C2×C4×D4 |
| prime radical | C2×C7×#41 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C7×#431 ◁ G | |
650 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)(8,9,11,10,12,13,15,14)(16,17,21,25)(18,23,27,30)(19,24,20,29)(22,28,31,26);(16,18)(17,22)(19,26)(20,28)(21,27)(23,29)(24,30)(25,31);(8,10,11,13,12,14,15,9)(16,18)(17,23)(19,28)(20,26)(21,27)(22,29)(24,31)(25,30);(16,19,21,20)(17,24,25,29)(18,26,27,28)(22,30,31,23)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 10864);