Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3057 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#21163 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | C2×C4×D4 |
| prime radical | C24×C7 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C22×C7×M16 ◁ G | |
882 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)(12,13,17,21,18,22,16,31)(14,19,26,34,24,33,25,40)(15,27,29,35,30,41,28,20)(23,36,39,42,37,43,38,32);(9,11)(12,14,17,26,18,24,16,25)(13,19,21,34,22,33,31,40)(15,23,29,39,30,37,28,38)(20,32,27,36,35,42,41,43);(12,15,16,28,18,30,17,29)(13,20,21,27,22,35,31,41)(14,23,25,38,24,37,26,39)(19,32,34,36,33,42,40,43);(14,24)(19,33)(23,37)(25,26)(32,42)(34,40)(36,43)(38,39)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14151);