Finite Group Databasebeta

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C2×C37×D165 #37567646

order24420
automorphism?
homologyAbelianization (H1) = C22×C37 · Schur multiplier (H2) = C2

Aliases

direct productC2×C37×D165
unambiguous semidirect product(C2×C3)⋊(C37×D55)
unambiguous semidirect product(C2×C5)⋊(C37×D33)
unambiguous semidirect product(C2×C11)⋊(D15×C37)

Splittings

Fitting, socleC2×C3×C5×C11×C37 ⋊ C2
derived, HallC3×C5×C11 ⋊ C22×C37
HallC3×C5×C11×C37 ⋊ C22
HallC5×C11×C37 ⋊ C2×D3
HallC3×C11×C37 ⋊ C2×D5
HallC3×C5×C37 ⋊ C2×D11
HallC11×C37 ⋊ C2×D15
HallC5×C37 ⋊ C2×D33
HallC3×C37 ⋊ C2×D55
HallC5×C11 ⋊ C2×D3×C37
HallC3×C11 ⋊ C2×D5×C37
HallC3×C5 ⋊ C2×D11×C37
SylowC11 ⋊ C2×D15×C37
SylowC5 ⋊ C2×C37×D33
SylowC3 ⋊ C2×C37×D55

Subgroups

subgroupG/H
center, hypercenterC2×C37D165
commutator, cosocle, hypocenterC3×C5×C11C22×C37
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C37C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C2×C37

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12210

Conjugacy classes & character table

6216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 167);