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D3×C37×C11⋊C5 #27131968

order12210
automorphism?
homologyAbelianization (H1) = C2×C5×C37 · Schur multiplier (H2) = C1

Aliases

direct productD3×C37×C11⋊C5
unambiguous semidirect productC3⋊(C2×C37×C11⋊C5)
unambiguous semidirect product(D3×C11)⋊(C5×C37)
unambiguous semidirect product(D3×C11×C37)⋊C5

Splittings

Fitting, socle, HallC3×C11×C37 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C5×C37
HallC3×C37×C11⋊C5 ⋊ C2
HallD3×C11×C37 ⋊ C5
HallC11×C37 ⋊ C5×D3
HallC3×C11⋊C5 ⋊ C2×C37
HallC3×C37 ⋊ C2×C11⋊C5
HallD3×C11 ⋊ C5×C37
SylowC11 ⋊ C5×D3×C37
SylowC3 ⋊ C2×C37×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC37D3×C11⋊C5
commutator, cosocle, hypocenterC3×C11C2×C5×C37
FrattiniC1G
Fitting, socleC3×C11×C37C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C37

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

777 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C37×AGL(1,𝔽11), D3×C37⋊AGL(1,𝔽11), D3×C11⋊C5×D37, …
maximal normal subgroup ofD3×C37×AGL(1,𝔽11), D3×C37⋊AGL(1,𝔽11), D3×C11⋊C5×D37, …
maximal quotient ofDic3×C37×C11⋊C5, C2×D3×C37×C11⋊C5, D9×C37×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12210, 23);