Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1795 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#10778 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #379 |
| commutator | C2×C4 | C2×C42×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| socle | C2×C7 | C22⋊#95 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
1164 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,20,23,15)(11,25,27,33)(12,18)(13,19)(14,17)(16,26,32,28)(21,35)(22,31,24,30)(29,36)(34,38)(37,39);(8,10,13,24,14,23,12,22)(9,15,19,31,17,20,18,30)(11,21,26,36,27,37,28,38)(16,29,25,39,32,34,33,35);(8,11)(9,16)(10,21)(12,28)(13,26)(14,27)(15,29)(17,32)(18,33)(19,25)(20,34)(22,38)(23,37)(24,36)(30,35)(31,39)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3766);