Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23439 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23522 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1326 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)(8,9)(10,11)(12,13)(14,22)(15,26)(16,30)(17,20)(18,24)(19,29)(21,32)(23,39)(25,37)(27,38)(28,36)(31,34)(33,42)(35,40)(41,43);(12,14,17,25)(13,18,20,34)(15,27,29,23)(16,31,32,24)(19,35,26,33)(21,37,30,22)(28,40,43,42)(36,38,41,39);(9,11)(12,15,16,28,17,29,32,43)(13,19,21,36,20,26,30,41)(14,23,24,40,25,27,31,42)(18,33,22,38,34,35,37,39);(13,20)(18,34)(19,26)(21,30)(22,37)(33,35)(36,41)(38,39)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16510);