Finite Group DatabasebetaFinite Group Databasebeta| order | 5528 |
| automorphism | Aut(G) order 3814320 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1382 |
| unambiguous semidirect product | C691⋊Q8 |
| Sylow | C691 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D691 |
| commutator, socle | C2×C691 | C22 |
| Fitting | C4×C691 | C2 |
| hypercenter | C4 | D691 |
| hypocenter | C691 | Q8 |
| LCS | G ▷ C2×C691 ▷ C691 | |
| UCS | C1 ◁ C2 ◁ C4 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,691|a^2=c,b^2=c,b^a=bc,d^b=d^6901385 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26010854, #26010855, #26010856, … |
| maximal normal subgroup of | #26010854, #26010855, #26010856, … |
| maximal quotient of | Dic691⋊C4, C4⋊Dic691, C2×Dic1382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5528, 11);