Finite Group Databasebeta

C2×#21426104 #28742726

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

Aliases

direct productC2×#21426104

Splittings

FittingC2×C59×#352 ⋊ C2
SylowC59 ⋊ C2×#2200

Subgroups

subgroupG/H
centerC22#16837590
commutator, cosocleC2×D4×C59C24
FrattiniC2×D4C23×D59
FittingC2×C59×#352C2
socleC22×C59B(4,𝔽2)
hypercenterC2×#352D59
hypocenterC59C2×#2200
LCSG ▷ C2×D4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#352

1328 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 323605);