Finite Group Databasebeta

C2×C4×#14268631 #28398983

order14464
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C4×#14268631

Splittings

SylowC113 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC2×C42C2×D113
commutatorC2×C113C22×C42
FrattiniC2×C4C23×D113
FittingC22×C42×C113C2
socleC23×C113C22×C4
prime radicalC24×C113C2×C4
cosocleC2×C4×C113C24
hypercenterC22×C42D113
hypocenterC113C2×C4×M16
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C42 ◁ C22×C42

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

3664 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 12919);