Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61569 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#61889 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C22×C7×D4 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C4×C7×Q8 ◁ G | |
1706 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,18)(11,15)(12,16)(13,17)(14,20)(19,23)(21,22)(24,25,28,32)(26,29,33,37)(27,30,35,31)(34,38,39,36);(8,10,13,20)(9,14,17,18)(11,19,12,21)(15,22,16,23)(24,26)(25,29)(27,34)(28,33)(30,38)(31,36)(32,37)(35,39);(8,11,13,12)(9,15,17,16)(10,19,20,21)(14,22,18,23)(25,30)(26,33)(27,35)(29,36)(31,32)(37,38);(8,12,13,11)(9,16,17,15)(10,19,20,21)(14,22,18,23);(9,17)(14,18)(15,16)(22,23)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54877);