Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | D7×#3026 |
| Fitting | C7×#3026 ⋊ C2 |
| Sylow | C7 ⋊ C2×#3026 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D7×#120 |
| commutator, cosocle | C23×C7 | C25 |
| Frattini | C23 | C24×D7 |
| Fitting | C7×#3026 | C2 |
| socle | C2×C7 | C22×#120 |
| hypercenter | #3026 | D7 |
| hypocenter | C7 | C2×#3026 |
| LCS | G ▷ C23×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C2 ◁ C24 ◁ #3026 | |
5318 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
145 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#3026 |
| maximal normal subgroup of | AGL(1,𝔽7)×#3026 |
| maximal quotient of | D7×#32898 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1036293);