Finite Group Databasebeta

C2×#20294941 #28366236

order13952
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20294941

Splittings

FittingC22×C22⋊C4×C109 ⋊ C2
SylowC109 ⋊ C2×#394

Subgroups

subgroupG/H
centerC24C22×D109
commutator, cosocleC23×C109C24
FrattiniC23C23×D109
FittingC22×C22⋊C4×C109C2
socleC24×C109C23
prime radicalC23×C22⋊D109C2
hypercenterC22×C22⋊C4D109
hypocenterC109C2×#394
LCSG ▷ C23×C109 ▷ C109
UCSC1 ◁ C24 ◁ C22×C22⋊C4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

2204 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 7714);