Finite Group DatabasebetaFinite Group Databasebeta| order | 8552 |
| automorphism | Aut(G) order 9133536 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2138 |
| unambiguous semidirect product | C1069⋊Q8 |
| Sylow | C1069 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1069 |
| commutator, socle | C2×C1069 | C22 |
| Fitting | C4×C1069 | C2 |
| hypercenter | C4 | D1069 |
| hypocenter | C1069 | Q8 |
| LCS | G ▷ C2×C1069 ▷ C1069 | |
| UCS | C1 ◁ C2 ◁ C4 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1069|a^2=c,b^2=c,b^a=bc,d^b=d^10682141 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30686020, #30686021, #30686022, … |
| maximal normal subgroup of | #30686020, #30686021, #30686022, … |
| maximal quotient of | #30686011, C4⋊Dic1069, C2×Dic2138, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8552, 11);