Finite Group Databasebeta

D59×#1753 #28586261

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productD59×#1753

Splittings

FittingC59×#1753 ⋊ C2
SylowC59 ⋊ C2×#1753

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D59
commutatorC22×C59C22×C42
FittingC59×#1753C2
socleC23×C59C23×C4
prime radicalC24×D59C2×C4
cosocleC22×C4×C59C24
hypercenter#1753D59
hypocenterC59C2×#1753
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #1753

1830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1736 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 167140);