Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1685 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C2×C7×#1700 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | #121 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G | |
650 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2)(27,28,29,30,31,32,33);(3,4,7,8)(5,10,9,6)(11,12)(13,19)(14,16)(15,23)(17,21)(18,22)(20,26)(24,25);(3,5,6,4,7,9,10,8)(12,16)(17,25)(18,23)(19,26);(4,8)(5,9)(11,13,14,20)(12,17,16,25)(15,24,22,21)(18,26,23,19)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12140);