Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2081 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C2×C7×#2081 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #397 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C23×C7×D4 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1006 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2)(19,20,21,22,23,24,25);(3,4,7,9,8,12,6,11)(5,13,15,18,14,17,16,10);(4,9)(5,14)(6,7)(10,17)(11,12)(13,18);(3,5,6,15,8,14,7,16)(4,10,11,13,12,18,9,17)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16638);