Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33557 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#33557 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C7 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C23×C7 ◁ C22×C7×D4 ◁ G | |
1258 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,15)(12,16)(13,18)(17,22)(19,21)(20,23);(8,10)(9,13)(11,18)(12,17)(14,15)(16,21)(19,20)(22,23);(8,10)(9,14)(11,19)(12,17)(13,15)(16,22)(18,20)(21,23);(10,17)(13,21)(14,22)(18,19)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26545);