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C3⋊((C11⋊C5)⋊Dic17) #26014348

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

Aliases

unambiguous semidirect productC3⋊((C11⋊C5)⋊Dic17)
unambiguous semidirect product(C11⋊C5)⋊Dic51
unambiguous semidirect productDic561⋊C5

Splittings

derived, HallC3×C11×C17 ⋊ C4×C5
HallC3×C17×C11⋊C5 ⋊ C4
HallDic561 ⋊ C5
HallC17×C11⋊C5 ⋊ Dic3
HallC11×C17 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ Dic17
HallC11⋊C5 ⋊ Dic51
HallC3×C17 ⋊ Dic11⋊C5
HallC3×C11 ⋊ C5×Dic17
SylowC17 ⋊ C3⋊(Dic11⋊C5)
SylowC11 ⋊ C5×Dic51
SylowC3 ⋊ (C11⋊C5)⋊Dic17

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C3⋊(C17⋊AGL(1,𝔽11))
commutator, hypocenterC3×C11×C17C4×C5
Fitting, socle, cosocleC2×C3×C11×C17C2×C5
prime radicalC2×C3×C17×C11⋊C5C2
LCSG ▷ C3×C11×C17
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

372 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9⋊((C11⋊C5)⋊Dic17), C3×C3⋊((C11⋊C5)⋊Dic17), C3⋊(C3⋊((C11⋊C5)⋊Dic17))
maximal normal subgroup ofC3×C3⋊((C11⋊C5)⋊Dic17)
maximal quotient ofC9⋊((C11⋊C5)⋊Dic17), C3×C3⋊((C11⋊C5)⋊Dic17), C3⋊(C3⋊((C11⋊C5)⋊Dic17))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 24);