Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25196 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#25196 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2424 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1032 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)(8,9,12,16,13,11,22,15)(10,17,20,18,21,23,19,14);(8,10,12,20,13,21,22,19)(9,14,16,17,11,18,15,23);(8,11)(9,13)(10,18)(12,16)(14,21)(15,22)(17,20)(19,23);(8,11)(9,13)(10,18)(12,15)(14,21)(16,22)(17,19)(20,23)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18184);