Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#10753 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | #120 |
| commutator | C2×C4 | C2×C42×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| socle | C22×C7 | #385 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C23×C4×C7 ◁ G | |
1166 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7)(8,9,10,11)(12,13,16,22,18,23,17,21)(14,24,28,33,27,34,26,19)(15,20,30,35,31,37,29,36)(25,39,40,32,41,38,42,43);(12,14,17,26,18,27,16,28)(13,19,21,34,23,33,22,24)(15,25,29,42,31,41,30,40)(20,32,36,39,37,43,35,38);(12,15)(13,20)(14,25)(16,30)(17,29)(18,31)(19,32)(21,36)(22,35)(23,37)(24,38)(26,42)(27,41)(28,40)(33,43)(34,39)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3741);