Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23990 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23992 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#585 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1128 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)(10,14,20,28)(11,15,21,29)(12,23,25,16)(18,31,24,26)(19,33,34,27)(22,36,35,30)(32,38,37,39);(10,18,20,24)(14,26,28,31)(19,32,34,37)(27,38,33,39);(8,10)(9,14)(11,19)(12,24)(13,20)(15,27)(16,31)(17,28)(18,25)(21,34)(22,37)(23,26)(29,33)(30,39)(32,35)(36,38);(8,11)(9,15)(10,19)(12,22)(13,21)(14,27)(16,30)(17,29)(18,32)(20,34)(23,36)(24,37)(25,35)(26,38)(28,33)(31,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16980);