Finite Group DatabasebetaFinite Group Databasebeta| order | 8764 |
| automorphism | Aut(G) order 8203104 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2191 |
| unambiguous semidirect product | C7⋊Dic313 |
| derived, Hall | C7×C313 ⋊ C4 |
| Sylow | C313 ⋊ Dic7 |
| Sylow | C7 ⋊ Dic313 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2191 |
| commutator, hypocenter | C7×C313 | C4 |
| Fitting, socle | C2×C7×C313 | C2 |
| LCS | G ▷ C7×C313 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,313,2|a^2=d,b^a=b^6,c^a=c^3122194 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2191, Dic6573, #39911446, … |
| maximal normal subgroup of | C3×Dic2191, #39911446, ΓL(1,𝔽8)⋊Dic313, … |
| maximal quotient of | C3×Dic2191, Dic6573, Dic15337 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8764, 4);