Finite Group Databasebeta

C2×#20295836 #28377791

order13952
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#20295836

Splittings

FittingC2×AGL(1,ℤ/8)×C109 ⋊ C2
SylowC109 ⋊ C2×#577

Subgroups

subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC4×C109C25
FrattiniC4C24×D109
FittingC2×AGL(1,ℤ/8)×C109C2
socleC22×C109C22×D4
hypercenterC2×AGL(1,ℤ/8)D109
hypocenterC109C2×#577
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

1460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 19269);