Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2021 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#11288 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | #120 |
| commutator | C24 | C22×C4×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| socle | C22×C7 | #385 |
| prime radical | C24×C7 | C22×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C23×C4×C7 ◁ G | |
602 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)(12,13,16,21,17,20,29,35)(14,18,24,32,23,31,27,36)(15,19,26,34,25,33,28,37)(22,30,39,41,38,42,40,43);(8,9)(10,11)(12,14)(13,18,20,31)(15,22,25,38)(16,27)(17,23)(19,30)(21,36,35,32)(24,29)(26,40,28,39)(33,42)(34,43)(37,41);(9,11)(12,15)(13,19,20,33)(14,22,23,38)(16,28)(17,25)(18,30)(21,37,35,34)(24,40,27,39)(26,29)(31,42)(32,43)(36,41)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 4276);