Finite Group Databasebeta

← Prev (#30633509) Next (#30633511) →

(C11⋊C5)⋊#64418 #30633510

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

Aliases

unambiguous semidirect product(C11⋊C5)⋊#64418
unambiguous semidirect product(C11⋊#64418)⋊C5

Splittings

Fitting, socle, HallC72×C11 ⋊ C5×D3
derived, HallC11×#3862 ⋊ C2×C5
HallC11⋊C5×#3862 ⋊ C2
HallC11⋊#64418 ⋊ C5
HallC72×C11⋊C5 ⋊ D3
Hall#3862 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ #64418
SylowC72 ⋊ C3⋊AGL(1,𝔽11)
SylowC11 ⋊ C5×#64418

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC11×#3862C2×C5
Fitting, socleC72×C11C5×D3
LCSG ▷ C11×#3862
UCSC1

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 154

Polycyclic presentation:

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

Conjugacy classes & character table

119 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×#64418, #64418⋊AGL(1,𝔽11), #20266354⋊C5, …
maximal normal subgroup ofAGL(1,𝔽11)×#64418, #64418⋊AGL(1,𝔽11), #20266354⋊C5, …
maximal quotient of(C11⋊C5)⋊#10596868, C2×(C11⋊C5)⋊#64418

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 55);