Finite Group Databasebeta

C2×#20295839 #28377795

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

Aliases

direct productC2×#20295839

Splittings

FittingC22×Q16×C109 ⋊ C2
SylowC109 ⋊ C2×#578

Subgroups

subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC4×C109C25
FrattiniC4C24×D109
FittingC22×Q16×C109C2
socleC22×C109C22×D4
hypercenterC22×Q16D109
hypocenterC109C2×#578
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

1408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

1556 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 19273);