Finite Group Databasebeta

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C2×C72×D165 #44568950

order32340
automorphism?
homologyAbelianization (H1) = C22×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C72×D165
unambiguous semidirect product(C2×C3)⋊(C72×D55)
unambiguous semidirect product(C2×C5)⋊(C72×D33)
unambiguous semidirect product(C2×C11)⋊(C72×D15)

Splittings

Fitting, socleC2×C3×C5×C72×C11 ⋊ C2
derived, HallC3×C5×C11 ⋊ C22×C72
HallC3×C5×C72×C11 ⋊ C22
HallC5×C72×C11 ⋊ C2×D3
HallC3×C72×C11 ⋊ C2×D5
HallC3×C5×C72 ⋊ C2×D11
HallC72×C11 ⋊ C2×D15
HallC5×C72 ⋊ C2×D33
HallC3×C72 ⋊ C2×D55
HallC5×C11 ⋊ C2×D3×C72
HallC3×C11 ⋊ C2×C72×D5
HallC3×C5 ⋊ C2×C72×D11
SylowC11 ⋊ C2×C72×D15
SylowC5 ⋊ C2×C72×D33
SylowC3 ⋊ C2×C72×D55

Subgroups

subgroupG/H
center, hypercenterC2×C72D165
commutator, cosocle, hypocenterC3×C5×C11C22×C72
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C11C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C2×C72

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16170

Conjugacy classes & character table

8232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 652);