Finite Group Databasebeta

C2×#21432640 #29452285

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#21432640

Splittings

FittingC22×#104×C59 ⋊ C2
SylowC59 ⋊ C2×#2901

Subgroups

subgroupG/H
centerC2×C4C2×D4×D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
FittingC22×#104×C59C2
socleC22×C59C22×C22⋊C4
prime radicalC2×#16838238C2
cosocleC2×C4×C59C25
hypercenterC22×#104D59
hypocenterC59C2×#2901
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

4946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1712 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1033164);