Finite Group Databasebeta

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C2×C3⋊(C11⋊(D37⋊C3)) #28410876

order14652
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊(C11⋊(D37⋊C3))
unambiguous semidirect product(C2×C3)⋊(C11⋊(D37⋊C3))
unambiguous semidirect product(C2×C11)⋊(C3⋊(D37⋊C3))
unambiguous semidirect product(C2×C37⋊C3)⋊D33
unambiguous semidirect product(C2×D1221)⋊C3

Splittings

Fitting, socleC2×C3×C11×C37 ⋊ C2×C3
derivedC3×C11×C37 ⋊ C22×C3
HallC3×C11×C37⋊C3 ⋊ C22
HallC11×C37 ⋊ C2×C3×D3
HallC3×C37⋊C3 ⋊ C2×D11
SylowC37 ⋊ C2×C3×D33
SylowC11 ⋊ C2×C3⋊(D37⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C11⋊(D37⋊C3))
commutator, cosocle, hypocenterC3×C11×C37C22×C3
FrattiniC1G
Fitting, socleC2×C3×C11×C37C2×C3
LCSG ▷ C3×C11×C37
UCSC1 ◁ C2

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2442

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14652, 91);