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D3×C72×C11⋊C5 #30633521

order16170
automorphism?
homologyAbelianization (H1) = C2×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productD3×C72×C11⋊C5
unambiguous semidirect productC3⋊(C2×C72×C11⋊C5)
unambiguous semidirect product(D3×C11)⋊(C5×C72)
unambiguous semidirect product(D3×C7×C11)⋊(C5×C7)
unambiguous semidirect product(D3×C72×C11)⋊C5

Splittings

Fitting, socle, HallC3×C72×C11 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C5×C72
HallC3×C72×C11⋊C5 ⋊ C2
HallD3×C72×C11 ⋊ C5
HallC72×C11 ⋊ C5×D3
HallC3×C11⋊C5 ⋊ C2×C72
HallC3×C72 ⋊ C2×C11⋊C5
HallD3×C11 ⋊ C5×C72
SylowC11 ⋊ C5×D3×C72
SylowC3 ⋊ C2×C72×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC72D3×C11⋊C5
commutator, cosocle, hypocenterC3×C11C2×C5×C72
FrattiniC1G
Fitting, socleC3×C72×C11C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C72

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1617

Conjugacy classes & character table

1029 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C72×AGL(1,𝔽11), D3×C7×C7⋊AGL(1,𝔽11), D3×C7×D7×C11⋊C5, …
maximal normal subgroup ofD3×C72×AGL(1,𝔽11), D3×C7×C7⋊AGL(1,𝔽11), D3×C7×D7×C11⋊C5, …
maximal quotient ofC72×Dic3×C11⋊C5, C2×D3×C72×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 66);