Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C2×C7×#2050 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | #124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | #394 |
| prime radical | C2×C7×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C23×C4×C7 ◁ G | |
1382 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)(5,12)(6,14)(7,15)(8,11)(9,13)(10,17)(16,18);(3,5)(4,9)(6,10)(7,16)(8,14)(11,18)(12,15)(13,17);(3,6,7,9,8,12,17,18)(4,5,10,13,11,14,15,16)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16514);