Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C22 |
| direct product | C2×H(7,𝔽2)⋊C7 |
| unambiguous semidirect product | (C2×H(7,𝔽2))⋊C7 |
| Fitting, Sylow | C2×H(7,𝔽2) ⋊ C7 |
| derived | H(7,𝔽2) ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C22 | #90632 |
| commutator, cosocle, hypocenter | H(7,𝔽2) | C2×C7 |
| Frattini | C2 | C2×#90632 |
| Fitting | C2×H(7,𝔽2) | C7 |
| LCS | G ▷ H(7,𝔽2) | |
| UCS | C1 ◁ C22 | |
4358 conjugacy classes of subgroups; only the 13 normal subgroups are shown.
This group has 4358 conjugacy classes of subgroups — too many to draw. Only its 13 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 32 |
46 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72209829 |
| maximal normal subgroup of | C2×#72209829 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1083545);