Finite Group DatabasebetaFinite Group Databasebeta| order | 5608 |
| automorphism | Aut(G) order 3925600 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2804 |
| unambiguous semidirect product | C4⋊D701 |
| Fitting | C4×C701 ⋊ C2 |
| Sylow | C701 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D701 |
| commutator, socle | C2×C701 | C22 |
| Fitting | C4×C701 | C2 |
| hypercenter | C4 | D701 |
| hypocenter | C701 | D4 |
| LCS | G ▷ C2×C701 ▷ C701 | |
| UCS | C1 ◁ C2 ◁ C4 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,701|b^a=bc,d^a=d^700,d^b=d^7001405 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26014291, D5608, #26014293, … |
| maximal normal subgroup of | #26014291, D5608, #26014293, … |
| maximal quotient of | #26014283, C4⋊Dic701, D5608, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5608, 10);