Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10046 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#10063 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C2×C7×#127 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G | |
670 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7)(12,13)(14,18)(15,17)(16,19)(20,21,24,27)(22,28,29,35)(23,31,32,26)(25,33,34,30);(8,9)(10,11)(13,17)(14,15)(18,19)(23,32)(26,31)(28,35)(30,33);(9,11)(12,14,16,15)(13,18,19,17)(20,22)(21,25)(23,33)(24,29)(26,35)(27,34)(28,31)(30,32)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3051);