Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | D7×#3498 |
| Fitting | C7×#3498 ⋊ C2 |
| Sylow | C7 ⋊ C2×#3498 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D7 |
| commutator, socle, cosocle | C22×C7 | C26 |
| Fitting | C7×#3498 | C2 |
| hypercenter | #3498 | D7 |
| hypocenter | C7 | C2×#3498 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ #3498 | |
12982 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#3498, D7×#62832, D7×#23872 |
| maximal normal subgroup of | AGL(1,𝔽7)×#3498, D7×#62832, D7×#23872 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1077883);