Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1685 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C2×C7×#1704 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | #121 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G | |
618 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2)(35,36,37,38,39,40,41);(3,4,7,10)(5,11,13,18)(6,15,12,9)(8,16,17,14)(19,20)(21,27)(22,24)(23,31)(25,29)(26,30)(28,34)(32,33);(3,5,12,16,7,13,6,14)(4,8,15,18,10,17,9,11)(20,24)(25,33)(26,31)(27,34);(5,13)(8,17)(11,18)(14,16)(19,21,22,28)(20,25,24,33)(23,32,30,29)(26,34,31,27)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12142);