Finite Group Databasebeta

C2×#21423211 #28564298

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21423211

Splittings

FittingC2×C59×#476 ⋊ C2
SylowC59 ⋊ C2×#1629

Subgroups

subgroupG/H
centerC23#14273695
commutator, cosocleC42×C59C24
FrattiniC42C23×D59
FittingC2×C59×#476C2
socleC23×C59#120
prime radicalC2×D4×D236C2
hypercenterC2×#476D59
hypocenterC59C2×#1629
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

1722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1154 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 145177);