Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#13321 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C7×#3058 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C2×C7×#131 ◁ G | |
552 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)(12,13,18,24)(14,25,28,40)(15,19,32,36)(16,23,17,22)(20,33,38,27)(21,31,35,29)(26,39,30,37)(34,42,41,43);(8,9)(10,11)(13,19)(15,29)(16,17)(20,34)(21,23)(22,35)(24,36)(25,39)(26,42)(27,33)(30,43)(31,32)(37,40)(38,41);(9,11)(12,14)(13,20)(15,30)(16,33)(17,27)(18,28)(19,34)(21,39)(22,40)(23,25)(24,38)(26,32)(29,43)(31,42)(35,37)(36,41)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6309);