Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#20935 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G | |
1690 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(9,11)(12,13)(14,15)(16,17,21,27,22,25,20,26)(18,28,32,23,30,38,31,39)(19,33,35,24,36,41,34,40)(29,37,45,42,43,47,44,46);(8,9,10,11)(16,18)(17,23)(19,29)(20,32)(21,31)(22,30)(24,37)(25,39)(26,38)(27,28)(33,42)(34,45)(35,44)(36,43)(40,47)(41,46);(13,15)(16,19,22,36)(17,24,25,40)(18,29,30,43)(20,35,21,34)(23,37,39,47)(26,41,27,33)(28,42,38,46)(31,45,32,44);(17,25)(18,30)(24,40)(26,27)(29,43)(31,32)(33,41)(44,45)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13923);