Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9239 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#9243 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C22×C7×D8 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
514 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,11,14,12,13,15,10)(16,17,20,23,21,25,19,24)(18,26,28,30,29,31,27,22);(8,10,11,13,12,14,15,9)(16,18)(17,22,25,30)(19,27)(20,28)(21,29)(23,26,24,31);(17,23)(19,20)(22,26)(24,25)(27,28)(30,31)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2231);