Finite Group Databasebeta

C2×#21425157 #28615691

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#21425157

Splittings

FittingC2×C59×#421 ⋊ C2
SylowC59 ⋊ C2×#2009

Subgroups

subgroupG/H
centerC22#16837311
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#421C2
socleC22×C59#392
prime radicalC2×#16838200C2
hypercenterC2×#421D59
hypocenterC59C2×#2009
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#421

1926 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, 196570);