Finite Group Databasebeta

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C4×#16813650 #28399386

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#16813650

Splittings

FittingC4×M16×C113 ⋊ C2
SylowC113 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4C2×D452
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
FittingC4×M16×C113C2
socleC22×C113C22×D4
prime radicalC2×#16813650C2
cosocleC2×C4×C113C24
hypercenterC4×M16D113
hypocenterC113C4×AGL(1,ℤ/8)
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

548 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, 13322);