Finite Group DatabasebetaFinite Group Databasebeta| order | 8936 |
| automorphism | Aut(G) order 9972576 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2234 |
| unambiguous semidirect product | C1117⋊Q8 |
| Sylow | C1117 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1117 |
| commutator, socle | C2×C1117 | C22 |
| Fitting | C4×C1117 | C2 |
| hypercenter | C4 | D1117 |
| hypocenter | C1117 | Q8 |
| LCS | G ▷ C2×C1117 ▷ C1117 | |
| UCS | C1 ◁ C2 ◁ C4 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1117|a^2=c,b^2=c,b^a=bc,d^b=d^11162237 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31821898, #31821899, #31821900, … |
| maximal normal subgroup of | #31821898, #31821899, #31821900, … |
| maximal quotient of | #31821889, C4⋊Dic1117, C2×Dic2234, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8936, 11);