Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#25189 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
1000 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)(12,13,18,22,19,23,17,33)(14,24,26,20,15,27,29,36)(16,30,31,21,32,37,34,38)(25,35,41,42,28,43,40,39);(8,9)(10,11)(12,14,18,26,19,15,17,29)(13,20,22,27,23,36,33,24)(16,25,31,41,32,28,34,40)(21,35,37,42,38,43,30,39);(9,11)(12,15)(13,20)(14,19)(16,28)(17,29)(18,26)(21,35)(22,24)(23,36)(25,32)(27,33)(30,42)(31,41)(34,40)(37,39)(38,43);(12,16,19,32)(13,21,23,38)(14,25,15,28)(17,34,18,31)(20,35,36,43)(22,37,33,30)(24,39,27,42)(26,41,29,40)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18177);