Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3055 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#21164 |
| 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 ◁ C23×C7×C8 ◁ G | |
890 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)(14,19,25,33,26,34,24,40)(15,27,30,35,28,41,29,20)(23,36,39,42,37,43,38,32);(9,11)(12,14,17,25,18,26,16,24)(13,19,21,33,22,34,31,40)(15,23,30,39,28,37,29,38)(20,32,27,36,35,42,41,43);(12,15,16,29,18,28,17,30)(13,20,21,27,22,35,31,41)(14,23,24,38,26,37,25,39)(19,32,33,36,34,42,40,43);(15,28)(20,35)(23,37)(27,41)(29,30)(32,42)(36,43)(38,39)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14152);