Finite Group DatabasebetaFinite Group Databasebeta| order | 11564 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C59 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic7×C59 |
| unambiguous semidirect product | C7⋊(C4×C7×C59) |
| derived | C7 ⋊ C4×C7×C59 |
| Hall | C72×C59 ⋊ C4 |
| Sylow | C72 ⋊ C4×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7×C59 | D7 |
| commutator, hypocenter | C7 | C4×C7×C59 |
| Frattini | C2 | C7×D7×C59 |
| Fitting, socle, prime radical | C2×C72×C59 | C2 |
| cosocle | C2×C7 | C2×C7×C59 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C7×C59 | |
36 conjugacy classes of subgroups.
4130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×C59×ΓL(1,𝔽8)⋊C4, C59×#10596873, C59×#10596872, … |
| maximal normal subgroup of | C7×C59×ΓL(1,𝔽8)⋊C4, C59×#10596873, C59×#10596872, … |
| maximal quotient of | C7×C59×Dic21, C3×C7×Dic7×C59 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11564, 12);