Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3057 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#20669 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | C22×C4⋊C4 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C22×C7×#41 ◁ G | |
1322 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13,17,21,18,22,16,31)(14,23,27,33,25,37,26,19)(15,20,30,35,28,34,29,41)(24,36,39,42,40,43,38,32);(12,14,16,26,18,25,17,27)(13,19,21,23,22,33,31,37)(15,24,29,38,28,40,30,39)(20,32,35,36,34,42,41,43);(9,11)(12,15)(13,20)(14,24)(16,29)(17,30)(18,28)(19,32)(21,35)(22,34)(23,36)(25,40)(26,38)(27,39)(31,41)(33,42)(37,43);(14,25)(15,28)(19,33)(20,34)(23,37)(26,27)(29,30)(35,41)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13657);