Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23439 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#23604 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1002 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2,3,4,5,6,7)(12,13,16,21,18,22,17,26)(14,23,25,27,15,20,24,19);(8,9)(10,11)(12,14,17,24,18,15,16,25)(13,19,21,23,22,27,26,20);(9,11)(12,15)(13,20)(14,18)(16,25)(17,24)(19,26)(21,27)(22,23);(12,16,18,17)(13,21,22,26)(14,24,15,25)(19,20,27,23)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16592);