Finite Group Databasebeta

D59×#2089 #28617796

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

Aliases

direct productD59×#2089

Splittings

FittingC59×#2089 ⋊ C2
SylowC59 ⋊ C2×#2089

Subgroups

subgroupG/H
centerC22#121×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2089C2
socleC22×C59C2×#121
prime radicalC23×D59#41
hypercenter#2089D59
hypocenterC59C2×#2089
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2089

810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 198675);