Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23892 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23892 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1674 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)(10,20)(11,26)(12,30)(13,18)(14,19)(15,23)(16,28)(17,27)(21,37)(22,32)(24,34)(25,33)(29,36)(31,38)(35,39);(8,10)(9,15)(11,22)(12,24)(13,23)(14,25)(16,35)(17,32)(18,33)(19,34)(20,30)(21,27)(26,31)(28,38)(29,39)(36,37);(8,11)(9,16)(10,21)(12,27)(13,28)(14,29)(15,31)(17,19)(18,36)(20,32)(22,23)(24,39)(25,38)(26,30)(33,35)(34,37);(8,11)(9,17)(10,22)(12,28)(13,27)(14,29)(15,32)(16,19)(18,36)(20,31)(21,23)(24,38)(25,39)(26,30)(33,37)(34,35)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16880);