Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#33689 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C7 |
| prime radical | C7×#575 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C2×C4×C7 ◁ C4×C7×M16 ◁ G | |
520 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,13,17)(10,18,20,36)(11,23,24,39)(12,28,26,16)(14,29,31,21)(15,33,34,27)(19,35,22,38)(25,30,37,32);(11,24)(15,34)(18,36)(21,29)(23,39)(25,37)(27,33)(35,38);(8,10)(9,14)(11,25)(12,19)(13,20)(15,35)(16,30)(17,31)(18,23)(21,27)(22,26)(24,37)(28,32)(29,33)(34,38)(36,39);(10,19,20,22)(11,24)(14,30,31,32)(15,34)(18,35,36,38)(21,25,29,37)(23,39)(27,33)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26677);