Finite Group DatabasebetaFinite Group Databasebeta| order | 8728 |
| automorphism | Aut(G) order 9513520 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2182 |
| unambiguous semidirect product | C1091⋊Q8 |
| Sylow | C1091 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1091 |
| commutator, socle | C2×C1091 | C22 |
| Fitting | C4×C1091 | C2 |
| hypercenter | C4 | D1091 |
| hypocenter | C1091 | Q8 |
| LCS | G ▷ C2×C1091 ▷ C1091 | |
| UCS | C1 ◁ C2 ◁ C4 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1091|a^2=c,b^2=c,b^a=bc,d^b=d^10902185 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31775396, #31775397, #31775398, … |
| maximal normal subgroup of | #31775396, #31775397, #31775398, … |
| maximal quotient of | Dic1091⋊C4, C4⋊Dic1091, C2×Dic2182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8728, 11);