Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32894 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#32895 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2846 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
3540 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)(9,15)(10,19)(12,13)(17,32)(18,24)(20,34)(21,26)(22,25)(27,30)(28,33)(29,38)(35,36);(8,9)(10,16)(11,17)(12,24)(13,15)(14,18)(19,30)(20,29)(21,31)(22,28)(23,33)(25,32)(26,27)(34,39)(35,37)(36,38);(8,10,14,21)(9,16,18,31)(11,20,23,36)(12,19,13,26)(15,27,24,30)(17,29,33,38)(22,35,25,34)(28,37,32,39);(8,11)(9,17)(10,20)(12,25)(13,22)(14,23)(15,28)(16,29)(18,33)(19,34)(21,36)(24,32)(26,35)(27,37)(30,39)(31,38)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 25883);