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C11×C3⋊#66775 #26014398

order11220
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC3×C5×C11×C17 ⋊ C4
derived, HallC3×C5×C17 ⋊ C4×C11
HallC5×C11×C17 ⋊ Dic3
HallC3×C11×C17 ⋊ AGL(1,𝔽5)
HallC11×C17 ⋊ ΓL(1,𝔽16)
HallC3×C5×C11 ⋊ #595
HallC5×C17 ⋊ C11×Dic3
HallC5×C11 ⋊ C3⋊#595
HallC3×C17 ⋊ C11×AGL(1,𝔽5)
HallC3×C11 ⋊ #66775
SylowC17 ⋊ C11×ΓL(1,𝔽16)
HallC3×C5 ⋊ C11×#595
SylowC5 ⋊ C11×C3⋊#595
SylowC3 ⋊ C11×#66775

Subgroups

subgroupG/H
center, hypercenterC11C3⋊#66775
commutator, hypocenterC3×C5×C17C4×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C17C4
prime radicalC3×C11×D85C2
cosocleC3×D85C2×C11
LCSG ▷ C3×C5×C17
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

759 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×C9⋊#66775, C3×C11×C3⋊#66775, C11×C3⋊(C3⋊#66775)
maximal normal subgroup ofC3×C11×C3⋊#66775
maximal quotient ofC11×C9⋊#66775, C3×C11×C3⋊#66775, C11×C3⋊(C3⋊#66775)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 74);