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(C11⋊C5)⋊#64424 #30633496

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C11⋊C5)⋊#64424
unambiguous semidirect product(C11⋊#64424)⋊C5

Splittings

Fitting, socle, derived, HallC72×C11 ⋊ C2×C3×C5
HallC11⋊C5×#3861 ⋊ C2
HallC7⋊(C7⋊AGL(1,𝔽11)) ⋊ C3
HallC11⋊#64424 ⋊ C5
HallC72×C11⋊C5 ⋊ C2×C3
HallC11×#3861 ⋊ C2×C5
HallC7⋊D77 ⋊ C3×C5
Hall#3861 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ #64424
SylowC72 ⋊ C3×AGL(1,𝔽11)
SylowC11 ⋊ C5×#64424

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC72×C11C2×C3×C5
LCSG ▷ C72×C11
UCSC1

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 539

Polycyclic presentation:

2,3,5,7^2,11|d^a=d^6,e^a=e^6,f^a=f^10,d^b=d^2,e^b=e^2,f^c=f^4

Conjugacy classes & character table

89 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×#64424, #64423⋊AGL(1,𝔽11), C2×(C11⋊C5)⋊#64424
maximal normal subgroup ofAGL(1,𝔽11)×#64424, #64423⋊AGL(1,𝔽11), C2×(C11⋊C5)⋊#64424
maximal quotient of(C11⋊C5)⋊#10596874, C2×(C11⋊C5)⋊#64424

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 41);