Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24390 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#25915 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#2619 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G | |
1110 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)(12,13,16,19)(14,18,15,17)(21,25)(22,29)(23,30)(26,33)(31,35)(32,34);(8,9)(10,11)(12,14,16,15)(13,17,19,18)(20,21,24,25)(22,26,31,32)(23,28,30,27)(29,34,35,33);(9,11)(12,14,16,15)(13,18,19,17)(20,22,30,35,24,31,23,29)(21,26,27,33,25,32,28,34);(12,15,16,14)(13,18,19,17)(20,23,24,30)(21,27,25,28)(22,29,31,35)(26,33,32,34)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18903);