Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33557 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#33558 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C7 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C23×C7 ◁ C22×C7×D4 ◁ G | |
1158 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,18)(11,15)(12,16)(13,17)(14,21)(19,31)(20,32)(22,28)(23,29)(24,37)(25,30)(26,33)(27,35)(34,39)(36,38);(8,10,13,20)(9,14,17,27)(11,19,22,34)(12,21,25,35)(15,26,28,38)(16,18,30,32)(23,33,24,36)(29,31,37,39);(8,11)(9,15)(10,19)(12,24)(13,22)(14,26)(16,29)(17,28)(18,31)(20,34)(21,36)(23,25)(27,38)(30,37)(32,39)(33,35);(10,20)(11,22)(14,27)(15,28)(18,32)(21,35)(23,24)(29,37)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26546);