Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23414 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C2×#127 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C2×#392 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
1980 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)(10,18)(11,15)(12,24)(13,17)(14,20)(16,26)(19,34)(21,32)(22,30)(23,38)(25,28)(27,39)(29,36)(31,37)(33,35);(8,10)(9,14)(11,19)(12,25)(13,21)(15,29)(16,32)(17,28)(18,24)(20,26)(22,35)(23,39)(27,30)(31,33)(34,38)(36,37);(8,11)(9,15)(10,19)(12,23)(13,22)(14,27)(16,31)(17,30)(18,33)(20,36)(21,35)(24,38)(25,39)(26,37)(28,29)(32,34);(11,22)(15,30)(19,35)(23,37)(27,29)(31,38)(33,34)(36,39)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16402);