Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2008 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C2×C7×#2008 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #392 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
2118 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)(5,13)(6,11)(7,10)(8,12)(9,14)(15,18)(16,17);(3,5)(4,9)(6,16)(7,14)(8,15)(10,18)(11,13)(12,17);(4,10)(6,7)(9,13)(11,12)(14,16)(17,18)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16398);