Finite Group DatabasebetaFinite Group Databasebeta| order | 5608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#14584149 |
| unambiguous semidirect product | D701⋊C4 |
| Fitting, socle | C2×C701 ⋊ C4 |
| derived, Sylow | C701 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #14584149 |
| commutator, hypocenter | C701 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C701 | C4 |
| LCS | G ▷ C701 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
358 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#14584149, C22⋊#14584149, C4⋊#14584149, … |
| maximal normal subgroup of | C4×#14584149, C22⋊#14584149, C4⋊#14584149, … |
| maximal quotient of | C4×#14584149, C22⋊#14584149, C4⋊#14584149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5608, 14);