Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C7×#11405 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C7×C8 | C42 |
| commutator | C4 | C2×C4×C7×C8 |
| Frattini, cosocle | C4×C8 | C23×C7 |
| socle | C22×C7 | C2×#97 |
| prime radical | C23×C7 | #97 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C7×C8 ◁ G | |
282 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)(16,17,19,23,20,25,31,39,21,24,32,38,33,40,46,47)(18,26,28,42,29,35,44,37,27,41,30,45,43,22,34,36);(8,9,10,12,11,13,14,15)(16,18)(17,22,24,35)(19,30)(20,29)(21,27)(23,37,38,36)(25,26,40,41)(28,32)(31,34)(33,43)(39,45,47,42)(44,46);(18,27)(22,35)(26,41)(28,30)(29,43)(34,44)(36,37)(42,45)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 4393);