Finite Group DatabasebetaFinite Group Databasebeta| order | 8764 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic313 |
| derived, Sylow | C313 ⋊ C4×C7 |
| Hall | C7×C313 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D313 |
| commutator, hypocenter | C313 | C4×C7 |
| Frattini | C2 | C7×D313 |
| Fitting, socle | C2×C7×C313 | C2 |
| LCS | G ▷ C313 | |
| UCS | C1 ◁ C2×C7 | |
12 conjugacy classes of subgroups.
2212 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×Dic313, C7×Dic939, C7×Dic313⋊C3, … |
| maximal normal subgroup of | C3×C7×Dic313, C7×Dic313⋊C3, ΓL(1,𝔽8)×Dic313, … |
| maximal quotient of | C3×C7×Dic313, C7×Dic939 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8764, 3);