Finite Group Databasebeta

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C3×C11⋊C5×D35 #26040488

order11550
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊C5×D35
unambiguous semidirect productC5⋊(C3×D7×C11⋊C5)
unambiguous semidirect product(C3×C11×D35)⋊C5

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C2×C5
derivedC5×C7×C11 ⋊ C2×C3×C5
HallC3×C5×C7×C11⋊C5 ⋊ C2
HallC5×C7×C11⋊C5 ⋊ C2×C3
HallC3×C5×C11⋊C5 ⋊ D7
HallC5×C11⋊C5 ⋊ C3×D7
HallC3×C7×C11 ⋊ C5×D5
HallC7×C11 ⋊ C3×C5×D5
HallC3×C11 ⋊ C5×D35
HallC3×C7 ⋊ D5×C11⋊C5
SylowC11 ⋊ C3×C5×D35
SylowC7 ⋊ C3×D5×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC3C11⋊C5×D35
commutator, cosocle, hypocenterC5×C7×C11C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C11C2×C5
LCSG ▷ C5×C7×C11
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

399 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D35×AGL(1,𝔽11), C3×D35⋊AGL(1,𝔽11), C3×D5×D7×C11⋊C5, …
maximal normal subgroup ofC3×D35×AGL(1,𝔽11), C3×D35⋊AGL(1,𝔽11), C3×D5×D7×C11⋊C5, …
maximal quotient ofC3×C11⋊C5×Dic35, C2×C3×C11⋊C5×D35, C9×C11⋊C5×D35, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 52);