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) = C24 |
| direct product | C7×#22931 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#121 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C4×C7×C22⋊C4 ◁ G | |
874 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(8,9,11,10)(13,16)(17,19)(20,21,24,29)(22,30,32,26)(23,28,25,27)(31,35,33,34);(8,10,11,9)(12,13)(14,17)(15,16)(18,19)(20,22)(21,26)(23,33)(24,32)(25,31)(27,34)(28,35)(29,30);(12,14,15,18)(13,17,16,19)(21,27)(23,25)(26,34)(28,29)(30,35)(31,33);(13,16)(17,19)(20,23,24,25)(21,28,29,27)(22,31,32,33)(26,34,30,35)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 15919);