Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C2×C7×#2014 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C7 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×#127 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ C22×C42×C7 ◁ G | |
2726 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2)(19,20,21,22,23,24,25);(3,4)(5,6)(11,12,15,18)(13,16,14,17);(4,6)(7,8)(9,10)(12,16)(13,14)(17,18);(8,10)(12,17)(13,14)(16,18)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16404);