Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18316 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18319 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C25×C7 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1058 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)(8,9,12,17)(10,19,22,32)(11,23,26,16)(13,18,27,15)(14,24,30,20)(21,34,37,35)(25,31,39,33)(28,36,29,38);(8,10,12,22)(9,14,17,30)(11,24,26,20)(13,21,27,37)(15,28,18,29)(16,32,23,19)(25,38,39,36)(31,34,33,35);(11,25)(16,33)(19,34)(20,36)(23,31)(24,38)(26,39)(32,35);(9,15)(14,28)(16,31)(17,18)(19,35)(23,33)(29,30)(32,34)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11307);