Finite Group Databasebeta

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C2×C11×C3⋊(D37⋊C3) #28410874

order14652
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×C3⋊(D37⋊C3)
unambiguous semidirect product(C2×C3)⋊(C11×D37⋊C3)
unambiguous semidirect product(C2×C37⋊C3)⋊(D3×C11)
unambiguous semidirect product(C2×D111)⋊(C3×C11)
unambiguous semidirect product(C2×C11×D111)⋊C3

Splittings

Fitting, socleC2×C3×C11×C37 ⋊ C2×C3
derivedC3×C37 ⋊ C22×C3×C11
HallC3×C11×C37⋊C3 ⋊ C22
HallC11×C37 ⋊ C2×C3×D3
HallC3×C37⋊C3 ⋊ C22×C11
SylowC37 ⋊ C2×C3×D3×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊(D37⋊C3)
commutator, cosocle, hypocenterC3×C37C22×C3×C11
FrattiniC1G
Fitting, socleC2×C3×C11×C37C2×C3
LCSG ▷ C3×C37
UCSC1 ◁ C2×C11

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2442

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14652, 89);