Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23860 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24259 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#546 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C4×C7×D4 ◁ G | |
1566 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)(12,13)(14,15)(16,17)(18,26)(19,22)(20,25)(21,24)(23,29)(27,30)(28,31);(8,9,11,10)(17,22)(18,27)(20,21)(23,26)(28,29)(30,31);(13,15)(16,18,19,28)(17,23,22,30)(20,27,21,29)(24,31,25,26);(8,10,11,9)(17,22)(18,28)(24,25)(27,29)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17247);