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C3×C11×#66775 #26014374

order11220
isoclinismisoclinic class of #66775
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×#66775

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C11#66775
commutator, hypocenterC5×C17C3×C4×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C17C4
prime radicalC3×C11×D85C2
cosocleD85C2×C3×C11
LCSG ▷ C5×C17
UCSC1 ◁ C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

825 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 50);