Finite Group DatabasebetaFinite Group Databasebeta| order | 11564 |
| isoclinism | isoclinic class of #5997 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C59 · Schur multiplier (H2) = C7 |
| direct product | C59×#5997 |
| Fitting, socle, Hall | C72×C59 ⋊ C4 |
| derived, Sylow | C72 ⋊ C4×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | #5997 |
| commutator, hypocenter | C72 | C4×C59 |
| Frattini | C1 | G |
| Fitting, socle | C72×C59 | C4 |
| prime radical | C59×C7⋊D7 | C2 |
| cosocle | C7⋊D7 | C2×C59 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C59 | |
28 conjugacy classes of subgroups.
944 conjugacy classes — view the full character table.
| maximal subgroup of | C59×#10596885, C59×#5997⋊C3, C3×C59×#5997, … |
| maximal normal subgroup of | C59×#5997⋊C3, C3×C59×#5997 |
| maximal quotient of | C3×C59×#5997, C59×C3⋊#5997 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11564, 22);