Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19713 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#19719 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
840 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(9,10)(11,12)(14,15)(17,21)(19,22)(23,27)(24,28)(26,29)(30,31);(8,9,12,15,13,14,11,10)(16,17,22,28,20,24,19,21)(18,23,29,31,25,30,26,27);(8,10,11,14,13,15,12,9)(16,18,20,25)(17,23,24,30)(19,26,22,29)(21,27,28,31);(9,14)(10,15)(18,25)(23,30)(26,29)(27,31)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12707);