Finite Group Databasebeta

D59×#1909 #28590658

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD59×#1909

Splittings

FittingC59×#1909 ⋊ C2
SylowC59 ⋊ C2×#1909

Subgroups

subgroupG/H
centerC2#386×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1909C2
socleC2×C59C2×#386
prime radicalC2×#41×D59C22
cosocleC22×C4×C59C24
hypercenter#1909D59
hypocenterC59C2×#1909
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1909

1686 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 171537);