Finite Group Databasebeta

C2×C4×#13182006 #28365363

order13952
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×#13182006

Splittings

FittingC22×C42×C109 ⋊ C2
SylowC109 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D109
commutatorC2×C109C22×C42
FrattiniC23C23×D109
FittingC22×C42×C109C2
socleC24×C109C23
prime radicalC24×D109C22
cosocleC23×C109C24
hypercenterC22×C42D109
hypocenterC109C2×C4×C22⋊C4
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

3536 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 6841);