Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#11929 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | #102 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C4×C8 | C23×C7 |
| socle | C22×C7 | C2×#102 |
| prime radical | C7×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,10,13,11,12,14,15)(16,17)(18,27)(19,24)(20,32)(21,36)(22,26)(23,29)(25,34)(28,43)(30,44)(31,42)(33,38)(35,46)(37,41)(39,47)(40,45);(9,12)(10,14)(16,18)(17,23)(19,28)(20,33)(21,37)(22,30)(24,38)(25,41)(26,40)(27,32)(29,34)(31,45)(35,47)(36,39)(42,43)(44,46);(16,19,22,21)(17,24,26,36)(18,28,30,37)(20,31,35,34)(23,38,40,39)(25,32,42,46)(27,43,44,41)(29,33,45,47)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 4917);