Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23504 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C23×C7 | C22×D4 |
| prime radical | C2×C7×#532 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ C22×C42×C7 ◁ G | |
1522 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)(13,14)(16,17)(18,26)(19,23)(20,24)(21,25)(22,29)(27,30)(28,31);(12,13)(14,15)(16,17)(18,27)(19,23)(20,24)(21,25)(22,28)(26,30)(29,31);(9,11)(12,14,15,13)(16,18)(17,22)(19,28)(20,29)(21,30)(23,26)(24,27)(25,31);(16,19,21,20)(17,23,25,24)(18,28,30,29)(22,26,31,27)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16492);