Finite Group Databasebeta

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D3×C53×C11⋊C5 #31775826

order17490
automorphism?
homologyAbelianization (H1) = C2×C5×C53 · Schur multiplier (H2) = C1

Aliases

direct productD3×C53×C11⋊C5
unambiguous semidirect productC3⋊(C2×C53×C11⋊C5)
unambiguous semidirect product(D3×C11)⋊(C5×C53)
unambiguous semidirect product(D3×C11×C53)⋊C5

Splittings

Fitting, socle, HallC3×C11×C53 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C5×C53
HallC3×C53×C11⋊C5 ⋊ C2
HallD3×C11×C53 ⋊ C5
HallC11×C53 ⋊ C5×D3
HallC3×C11⋊C5 ⋊ C2×C53
HallC3×C53 ⋊ C2×C11⋊C5
HallD3×C11 ⋊ C5×C53
SylowC11 ⋊ C5×D3×C53
SylowC3 ⋊ C2×C53×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC53D3×C11⋊C5
commutator, cosocle, hypocenterC3×C11C2×C5×C53
FrattiniC1G
Fitting, socleC3×C11×C53C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C53

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1749

Conjugacy classes & character table

1113 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C53×AGL(1,𝔽11), D3×C53⋊AGL(1,𝔽11), D3×C11⋊C5×D53, …
maximal normal subgroup ofD3×C53×AGL(1,𝔽11), D3×C53⋊AGL(1,𝔽11), D3×C11⋊C5×D53, …
maximal quotient ofDic3×C53×C11⋊C5, C2×D3×C53×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 21);