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×#10767 |
| 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 | |
1148 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)(8,9,12,19,14,18,13,17)(10,20,23,30,24,31,22,15)(11,25,27,33,28,16,26,32)(21,35,36,39,37,34,38,29);(8,10,13,22,14,24,12,23)(9,15,17,31,18,30,19,20)(11,21,27,36,28,37,26,38)(16,29,32,35,25,39,33,34);(8,11)(9,16)(10,21)(12,26)(13,27)(14,28)(15,29)(17,32)(18,25)(19,33)(20,34)(22,36)(23,38)(24,37)(30,39)(31,35)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3755);