Finite Group Databasebeta

C2×#21435886 #29464904

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#21435886

Splittings

FittingC2×C59×#456 ⋊ C2
SylowC59 ⋊ C2×#3291

Subgroups

subgroupG/H
centerC22#16838034
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#456C2
socleC22×C59D42
hypercenterC2×#456D59
hypocenterC59C2×#3291
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#456

2682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1045783);