Finite Group Databasebeta

C2×D4×D452 #28404014

order14464
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×D4×D452

Splittings

FittingC2×C4×D4×C113 ⋊ C2
SylowC113 ⋊ C2×D42

Subgroups

subgroupG/H
centerC23C23×D113
commutator, cosocleC22×C113C25
FrattiniC22C24×D113
FittingC2×C4×D4×C113C2
socleC23×C113C24
hypercenterC2×C4×D4D113
hypocenterC113C2×D42
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×C4×D4

2536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Conjugacy classes & character table

2290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 17950);