Finite Group Databasebeta

D59×#3020 #29455330

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productD59×#3020

Splittings

FittingC59×#3020 ⋊ C2
SylowC59 ⋊ C2×#3020

Subgroups

subgroupG/H
centerC2C2×#120×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#3020C2
socleC2×C59C22×#120
hypercenter#3020D59
hypocenterC59C2×#3020
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22×C4 ◁ #3020

4710 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, 1036209);