Finite Group Databasebeta

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C4×#19153843 #37542530

order23168
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#19153843

Splittings

FittingC4×SD16×C181 ⋊ C2
SylowC181 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4D4×D181
commutatorC4×C181C23×C4
FrattiniC2×C4C23×D181
FittingC4×SD16×C181C2
socleC22×C181C22×D4
prime radicalC2×#19153843C2
cosocleC2×C4×C181C24
hypercenterC4×SD16D181
hypocenterC181C4×AGL(1,ℤ/8)
LCSG ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5792

Conjugacy classes & character table

2564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 13319);