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C3×C11⋊#66775 #26014378

order11220
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊#66775
unambiguous semidirect productC11⋊(C3×#66775)

Splittings

Fitting, socle, HallC3×C5×C11×C17 ⋊ C4
derived, HallC5×C11×C17 ⋊ C3×C4
HallC3×C11×C17 ⋊ AGL(1,𝔽5)
HallC3×C5×C17 ⋊ Dic11
HallC11×C17 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C11 ⋊ #595
HallC5×C17 ⋊ C3×Dic11
HallC5×C11 ⋊ C3×#595
HallC3×C17 ⋊ C11⋊AGL(1,𝔽5)
HallC3×C11 ⋊ #66775
SylowC17 ⋊ C3×C11⋊AGL(1,𝔽5)
HallC3×C5 ⋊ C11⋊#595
SylowC11 ⋊ C3×#66775
SylowC5 ⋊ C3×C11⋊#595

Subgroups

subgroupG/H
center, hypercenterC3C11⋊#66775
commutator, hypocenterC5×C11×C17C3×C4
FrattiniC1G
Fitting, socleC3×C5×C11×C17C4
prime radicalC3×C11×D85C2
cosocleC11×D85C2×C3
LCSG ▷ C5×C11×C17
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

735 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×C11⋊#66775, C32×C11⋊#66775, C3×C3⋊(C11⋊#66775)
maximal normal subgroup ofC9×C11⋊#66775, C32×C11⋊#66775
maximal quotient ofC9×C11⋊#66775, C32×C11⋊#66775, C3×C3⋊(C11⋊#66775)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 54);