Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23998 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23998 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1266 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)(10,16)(11,20)(12,15)(13,19)(14,22)(17,21)(18,23);(8,9)(10,17,18,13)(11,14)(12,15)(16,19,23,21)(20,22);(8,10)(9,13)(11,21)(12,18)(14,23)(15,17)(16,20)(19,22);(11,22)(14,20)(16,23)(19,21)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16986);