Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C2×C7×#2051 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×AGL(1,ℤ/8) | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C23×C4×C7 ◁ G | |
1490 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2)(23,24,25,26,27,28,29);(3,4)(5,6)(7,8)(9,17)(10,13)(11,15)(12,16)(14,20)(18,21)(19,22);(8,13)(9,18)(10,11)(14,17)(15,16)(21,22);(4,6)(7,9,10,19,12,18,11,20)(8,14,15,21,16,22,13,17)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16516);