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C5×C11×C3⋊#595 #26014389

order11220
isoclinismisoclinic class of C3⋊#595
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×C3⋊#595
unambiguous semidirect productC3⋊(C5×C11×#595)

Splittings

Fitting, socle, HallC3×C5×C11×C17 ⋊ C4
derived, HallC3×C17 ⋊ C4×C5×C11
HallC5×C11×C17 ⋊ Dic3
HallC3×C11×C17 ⋊ C4×C5
HallC3×C5×C17 ⋊ C4×C11
HallC11×C17 ⋊ C5×Dic3
HallC3×C5×C11 ⋊ #595
HallC5×C17 ⋊ C11×Dic3
HallC3×C11 ⋊ C5×#595
SylowC17 ⋊ C5×C11×Dic3
HallC3×C5 ⋊ C11×#595
SylowC3 ⋊ C5×C11×#595

Subgroups

subgroupG/H
center, hypercenterC5×C11C3⋊#595
commutator, hypocenterC3×C17C4×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C17C4
prime radicalC3×C5×C11×D17C2
cosocleC3×D17C2×C5×C11
LCSG ▷ C3×C17
UCSC1 ◁ C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

990 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C11×C9⋊#595, C3×C5×C11×C3⋊#595, C5×C11×C3⋊(C3⋊#595)
maximal normal subgroup ofC3×C5×C11×C3⋊#595
maximal quotient ofC5×C11×C9⋊#595, C3×C5×C11×C3⋊#595, C5×C11×C3⋊(C3⋊#595)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 65);