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) = C23×C4 |
| direct product | C7×#22140 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C23×C7 | C23×C4 |
| prime radical | C7×#392 | C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
856 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(13,16)(14,18)(20,21,25,29,24,28,23,27)(22,26,30,33,31,34,32,35);(12,13,15,16)(14,17,18,19)(20,21,23,27,24,28,25,29)(22,26,32,35,31,34,30,33);(9,11)(13,16)(17,19)(20,22)(21,26)(23,32)(24,31)(25,30)(27,35)(28,34)(29,33);(12,14,15,18)(13,17,16,19)(20,23,24,25)(21,27,28,29)(22,30,31,32)(26,33,34,35)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 15128);