Finite Group Databasebeta

D59×#2019 #28615877

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productD59×#2019

Splittings

FittingC59×#2019 ⋊ C2
SylowC59 ⋊ C2×#2019

Subgroups

subgroupG/H
centerC22#121×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2019C2
socleC22×C59C2×#121
prime radicalC2×AGL(1,ℤ/8)×D59C2
hypercenter#2019D59
hypocenterC59C2×#2019
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2019

2030 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

806 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 196756);