Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C2×C43 |
| direct product | C7×#14677 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C7 | C24 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C24 | C24×C7 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
1182 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(16,17,20,18)(19,21,23,22)(24,25)(26,28)(27,29)(30,31);(9,11)(12,13,14,15)(17,18)(19,23)(25,26)(29,30);(8,9,10,11)(16,18,20,17)(19,21,23,22)(24,26,28,25)(27,29,31,30);(16,19,20,23)(17,21,18,22)(24,27,28,31)(25,29,26,30)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 7665);