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C3×C7×D5×C11⋊C5 #26040486

order11550
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D5×C11⋊C5
unambiguous semidirect productC5⋊(C2×C3×C7×C11⋊C5)
unambiguous semidirect product(D5×C11)⋊(C3×C5×C7)
unambiguous semidirect product(C3×D5×C11)⋊(C5×C7)
unambiguous semidirect product(C3×C7×D5×C11)⋊C5

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C7D5×C11⋊C5
commutator, cosocle, hypocenterC5×C11C2×C3×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C11C2×C5
LCSG ▷ C5×C11
UCSC1 ◁ C3×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

588 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C7×(C11⋊C5)⋊AGL(1,𝔽5), C3×C7×AGL(1,𝔽5)×C11⋊C5, C3×C7⋊((C11⋊C5)⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC3×C7×(C11⋊C5)⋊AGL(1,𝔽5), C3×C7×AGL(1,𝔽5)×C11⋊C5, C3×C7⋊((C11⋊C5)⋊AGL(1,𝔽5)), …
maximal quotient ofC3×C7×Dic5×C11⋊C5, C2×C3×C7×D5×C11⋊C5, C7×C9×D5×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 50);