Finite Group Databasebeta

C2×#21425564 #28617635

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21425564

Splittings

SylowC59 ⋊ C2×#2082

Subgroups

subgroupG/H
centerC22#16837330
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#419C2
socleC22×C59#397
prime radicalC24×C59#41
hypercenterC2×#419D59
hypocenterC59C2×#2082
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#419

878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1322 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 198514);