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C17×C3⋊(Dic11⋊C5) #26014347

order11220
automorphism?
homologyAbelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×C3⋊(Dic11⋊C5)
unambiguous semidirect productC3⋊(C17×Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(Dic3×C17)
unambiguous semidirect productDic33⋊(C5×C17)
unambiguous semidirect product(C17×Dic33)⋊C5

Splittings

derived, HallC3×C11 ⋊ C4×C5×C17
HallC3×C17×C11⋊C5 ⋊ C4
HallC17×Dic33 ⋊ C5
HallC17×C11⋊C5 ⋊ Dic3
HallC3×C11×C17 ⋊ C4×C5
HallC11×C17 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ C4×C17
HallDic33 ⋊ C5×C17
HallC11⋊C5 ⋊ Dic3×C17
HallC3×C17 ⋊ Dic11⋊C5
SylowC11 ⋊ C5×Dic3×C17
SylowC3 ⋊ C17×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C17C3⋊AGL(1,𝔽11)
commutator, hypocenterC3×C11C4×C5×C17
FrattiniC2C17×C3⋊AGL(1,𝔽11)
Fitting, socleC2×C3×C11×C17C2×C5
prime radicalC2×C3×C17×C11⋊C5C2
cosocleC2×C3×C11C2×C5×C17
LCSG ▷ C3×C11
UCSC1 ◁ C2×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

612 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC17×C9⋊(Dic11⋊C5), C3×C17×C3⋊(Dic11⋊C5), C17×C3⋊(C3⋊(Dic11⋊C5))
maximal normal subgroup ofC3×C17×C3⋊(Dic11⋊C5)
maximal quotient ofC17×C9⋊(Dic11⋊C5), C3×C17×C3⋊(Dic11⋊C5), C17×C3⋊(C3⋊(Dic11⋊C5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 23);