Finite Group Databasebeta

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C3×C11⋊C5×D53 #31775823

order17490
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊C5×D53
unambiguous semidirect productC53⋊(C2×C3×C11⋊C5)
unambiguous semidirect product(C11×D53)⋊(C3×C5)
unambiguous semidirect product(C3×C11×D53)⋊C5

Splittings

Fitting, socle, HallC3×C11×C53 ⋊ C2×C5
derived, HallC11×C53 ⋊ C2×C3×C5
HallC3×C53×C11⋊C5 ⋊ C2
HallC3×C11×D53 ⋊ C5
HallC53×C11⋊C5 ⋊ C2×C3
HallC11×D53 ⋊ C3×C5
HallC3×C53 ⋊ C2×C11⋊C5
SylowC53 ⋊ C2×C3×C11⋊C5
HallC3×C11 ⋊ C5×D53
SylowC11 ⋊ C3×C5×D53

Subgroups

subgroupG/H
center, hypercenterC3C11⋊C5×D53
commutator, cosocle, hypocenterC11×C53C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C53C2×C5
LCSG ▷ C11×C53
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1749

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×(C11⋊C5)⋊#6157, C3×D53×AGL(1,𝔽11), C3×C11⋊C5×#6157, …
maximal normal subgroup ofC3×(C11⋊C5)⋊#6157, C3×D53×AGL(1,𝔽11), C3×C11⋊C5×#6157, …
maximal quotient ofC3×C11⋊C5×Dic53, C2×C3×C11⋊C5×D53

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 18);