Finite Group DatabasebetaFinite Group Databasebeta| order | 5608 |
| automorphism | Aut(G) order 3925600 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1402 |
| unambiguous semidirect product | C701⋊Q8 |
| Sylow | C701 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D701 |
| commutator, socle | C2×C701 | C22 |
| Fitting | C4×C701 | C2 |
| hypercenter | C4 | D701 |
| hypocenter | C701 | Q8 |
| LCS | G ▷ C2×C701 ▷ C701 | |
| UCS | C1 ◁ C2 ◁ C4 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,701|a^2=c,b^2=c,b^a=bc,d^b=d^7001405 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26014294, #26014295, #26014296, … |
| maximal normal subgroup of | #26014294, #26014295, #26014296, … |
| maximal quotient of | #26014285, C4⋊Dic701, C2×Dic1402, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5608, 11);