Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10603 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#10606 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #396 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C23×C7 | C22⋊Q8 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
306 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,10,15,12,11,13,14)(16,17)(18,26)(19,24)(20,23)(21,25)(22,28)(27,30)(29,31);(8,10,12,13)(9,14,11,15)(16,18,19,28,21,27,20,29)(17,22,23,26,25,31,24,30);(8,11,12,9)(10,15,13,14)(17,23)(18,27)(19,20)(22,26)(24,25)(30,31)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3594);