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C3⋊((C11⋊C5)⋊#595) #26014353

order11220
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊((C11⋊C5)⋊#595)
unambiguous semidirect product(C11⋊C5)⋊(C3⋊#595)
unambiguous semidirect product(C3⋊(C11⋊#595))⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C17 ⋊ C4×C5
HallC3×C17×C11⋊C5 ⋊ C4
HallC3⋊(C11⋊#595) ⋊ C5
HallC17×C11⋊C5 ⋊ Dic3
HallC11×C17 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ #595
HallC11⋊C5 ⋊ C3⋊#595
HallC3×C17 ⋊ Dic11⋊C5
HallC3×C11 ⋊ C5×#595
SylowC17 ⋊ C3⋊(Dic11⋊C5)
SylowC11 ⋊ C5×C3⋊#595
SylowC3 ⋊ (C11⋊C5)⋊#595

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C11×C17C4×C5
prime radicalC3×D17×C11⋊C5C2
cosocleC3×C11×D17C2×C5
LCSG ▷ C3×C11×C17
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,5,2,3,11,17|a^2=c,d^a=d^2,e^a=e^10,f^a=f^13,e^b=e^4,f^c=f^16

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9⋊((C11⋊C5)⋊#595), C3×C3⋊((C11⋊C5)⋊#595), C3⋊(C3⋊((C11⋊C5)⋊#595))
maximal normal subgroup ofC3×C3⋊((C11⋊C5)⋊#595)
maximal quotient ofC9⋊((C11⋊C5)⋊#595), C3×C3⋊((C11⋊C5)⋊#595), C3⋊(C3⋊((C11⋊C5)⋊#595))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 29);