Finite Group Databasebeta

C2×#21425366 #28616516

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

Aliases

direct productC2×#21425366

Splittings

SylowC59 ⋊ C2×#2048

Subgroups

subgroupG/H
centerC22#16837316
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
Fitting, prime radicalC22×AGL(1,ℤ/8)×C59C2
socleC22×C59#394
hypercenterC22×AGL(1,ℤ/8)D59
hypocenterC59C2×#2048
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

1450 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 197395);