Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | D7×#3585 |
| Fitting | C7×#3585 ⋊ C2 |
| Sylow | C7 ⋊ C2×#3585 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×D4×D7 |
| commutator, cosocle | C4×C7 | C26 |
| Frattini | C4 | C25×D7 |
| Fitting | C7×#3585 | C2 |
| socle | C2×C7 | C24×D4 |
| hypercenter | #3585 | D7 |
| hypocenter | C7 | C2×#3585 |
| LCS | G ▷ C4×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #3585 | |
11138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
205 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#61110, D7×#23882, AGL(1,𝔽7)×#3585, … |
| maximal normal subgroup of | D7×#61110, D7×#23882, AGL(1,𝔽7)×#3585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1083403);