Finite Group DatabasebetaFinite Group Databasebeta| order | 11564 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C59⋊#5997 |
| Fitting, socle, derived, Hall | C72×C59 ⋊ C4 |
| Sylow | C59 ⋊ #5997 |
| Sylow | C72 ⋊ Dic59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C59 | C4 |
| prime radical, cosocle | C59×C7⋊D7 | C2 |
| LCS | G ▷ C72×C59 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,7^2,59|a^2=b,c^a=c^4d^6,d^a=c^3d^3,e^a=e^58,c^b=c^6,d^b=d^6770 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, C3⋊(C59⋊#5997) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11564, 23);