Finite Group Databasebeta

C2×#21426090 #28742702

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

Aliases

direct productC2×#21426090

Splittings

FittingC2×C59×#458 ⋊ C2
SylowC59 ⋊ C2×#2198

Subgroups

subgroupG/H
centerC22#16837588
commutator, cosocleC2×D4×C59C24
FrattiniC2×D4C23×D59
FittingC2×C59×#458C2
socleC22×C59B(4,𝔽2)
prime radicalC2×#16837570C2
hypercenterC2×#458D59
hypocenterC59C2×#2198
LCSG ▷ C2×D4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#458

1244 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 323581);