Finite Group DatabasebetaFinite Group Databasebeta| order | 11564 |
| isoclinism | isoclinic class of D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×Dic59 |
| unambiguous semidirect product | C59⋊(C4×C72) |
| derived, Sylow | C59 ⋊ C4×C72 |
| Hall | C72×C59 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C72 | D59 |
| commutator, hypocenter | C59 | C4×C72 |
| Frattini | C2 | C72×D59 |
| Fitting, socle, prime radical | C2×C72×C59 | C2 |
| cosocle | C2×C59 | C2×C72 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C2×C72 | |
60 conjugacy classes of subgroups.
3038 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×ΓL(1,𝔽8)×Dic59, #3861×Dic59, #3862×Dic59, … |
| maximal normal subgroup of | C7×ΓL(1,𝔽8)×Dic59, #3861×Dic59, #3862×Dic59, … |
| maximal quotient of | C72×Dic177, C3×C72×Dic59 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11564, 11);