Finite Group Databasebeta

C2×C4×#13182013 #28371441

order13952
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C4×#13182013

Splittings

SylowC109 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC2×C42C2×D109
commutatorC2×C109C22×C42
FrattiniC2×C4C23×D109
FittingC22×C42×C109C2
socleC23×C109C22×C4
prime radicalC24×C109C2×C4
cosocleC2×C4×C109C24
hypercenterC22×C42D109
hypocenterC109C2×C4×M16
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C42 ◁ C22×C42

656 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, 12919);