Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32894 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#32896 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2846 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×H(7,𝔽2) | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
3610 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)(8,9,14,20)(10,21,24,34)(11,17,26,33)(12,19,13,18)(15,27,31,23)(16,28,32,25)(22,29,39,36)(30,38,35,37);(8,10)(9,15)(11,22)(12,27)(13,23)(14,24)(16,29)(17,30)(18,34)(19,21)(20,31)(25,38)(26,39)(28,37)(32,36)(33,35);(8,11)(9,16)(10,22)(12,25)(13,28)(14,26)(15,29)(17,18)(19,33)(20,32)(21,35)(23,37)(24,39)(27,38)(30,34)(31,36);(8,11)(9,17)(10,22)(12,28)(13,25)(14,26)(15,30)(16,18)(19,32)(20,33)(21,36)(23,38)(24,39)(27,37)(29,34)(31,35)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 25884);