Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23408 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3449 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1946 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(12,13,18,23)(14,24,26,36)(15,28,30,37)(16,22,17,21)(19,31,34,27)(20,32,35,29)(25,33,39,43)(38,40,42,41);(8,9)(10,11)(12,14)(13,19)(15,25)(16,31)(17,27)(18,26)(20,33)(21,36)(22,24)(23,34)(28,42)(29,41)(30,39)(32,40)(35,43)(37,38);(9,11)(12,15)(13,20)(14,25)(16,29)(17,32)(18,30)(19,33)(21,28)(22,37)(23,35)(24,38)(26,39)(27,40)(31,41)(34,43)(36,42);(14,26)(19,34)(24,36)(25,39)(27,31)(33,43)(38,42)(40,41)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16396);