Finite Group DatabasebetaFinite Group Databasebeta| order | 8776 |
| automorphism | Aut(G) order 9618496 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2194 |
| unambiguous semidirect product | C1097⋊Q8 |
| Sylow | C1097 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1097 |
| commutator, socle | C2×C1097 | C22 |
| Fitting | C4×C1097 | C2 |
| hypercenter | C4 | D1097 |
| hypocenter | C1097 | Q8 |
| LCS | G ▷ C2×C1097 ▷ C1097 | |
| UCS | C1 ◁ C2 ◁ C4 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1097|a^2=c,b^2=c,b^a=bc,d^b=d^10962197 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31798152, #31798153, #31798154, … |
| maximal normal subgroup of | #31798152, #31798153, #31798154, … |
| maximal quotient of | #31798143, C4⋊Dic1097, C2×Dic2194, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8776, 11);