Finite Group Databasebeta

C2×#20298354 #28390274

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

Aliases

direct productC2×#20298354

Splittings

SylowC113 ⋊ C2×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC2×C4C4×Dic113
commutatorC4×C113C2×C42
FrattiniC22×C4C22×D113
FittingC2×#117×C113C2
socleC22×C113#95
prime radicalC24×C113D4
cosocleC22×C4×C113C23
hypercenterC2×#117D113
hypocenterC113C2×H(3,ℤ/4)
LCSG ▷ C4×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C2×#117

404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Conjugacy classes & character table

2284 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 4210);