Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13391 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13391 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2033 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C7×#3067 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ C2×C7×#131 ◁ G | |
390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,21)(11,25)(12,27)(13,29)(14,18)(15,20)(16,22)(17,26)(19,28)(23,33)(24,34)(30,32)(31,35)(36,39)(37,38);(8,10)(9,16)(11,12)(13,23)(14,22)(15,24)(17,35)(18,34)(19,33)(20,25)(21,27)(26,28)(29,37)(30,38)(31,39)(32,36);(8,11,12,10,15,22,14,24)(9,17,18,36,20,37,27,33)(13,23,28,38,31,39,30,26)(16,32,21,35,25,19,34,29)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6379);