Finite Group Databasebeta

C2×#20299465 #28406243

order14464
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#20299465

Splittings

FittingC2×C42×C113 ⋊ C4
SylowC113 ⋊ C2×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC2×C4C4×#90673
commutatorC4×C113C2×C42
FrattiniC2×C4C22×#90673
FittingC2×C42×C113C4
socleC22×C113#95
prime radicalC23×D113D4
cosocleC2×C4×D113C23
hypercenterC2×C42#90673
hypocenterC113C2×H(3,ℤ/4)
LCSG ▷ C4×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C2×C42

404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 20179);