Finite Group DatabasebetaFinite Group Databasebeta| order | 8764 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#11929411 |
| Fitting, socle, derived, Hall | C7×C313 ⋊ C4 |
| Sylow | C313 ⋊ Dic7 |
| Sylow | C7 ⋊ #11929411 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C313 | C4 |
| LCS | G ▷ C7×C313 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,7,313|a^2=b,c^a=c^6,d^a=d^288,d^b=d^312556 conjugacy classes — view the full character table.
| maximal subgroup of | #39911452, #39911453, ΓL(1,𝔽8)⋊#11929411, … |
| maximal normal subgroup of | #39911452, #39911453, ΓL(1,𝔽8)⋊#11929411, … |
| maximal quotient of | C3×C7⋊#11929411, C3⋊(C7⋊#11929411) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8764, 7);