Finite Group Databasebeta

← Prev (#36348651) Next (#36348653) →

(C11⋊C5)⋊(D67⋊C3) #36348652

order22110
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C11⋊C5)⋊(D67⋊C3)
unambiguous semidirect product(C67⋊C3)⋊AGL(1,𝔽11)
unambiguous semidirect product(C11⋊(D67⋊C3))⋊C5
unambiguous semidirect product((C11⋊C5)⋊D67)⋊C3

Splittings

Fitting, socle, derived, HallC11×C67 ⋊ C2×C3×C5
HallC11⋊C5×C67⋊C3 ⋊ C2
Hall(C11⋊C5)⋊D67 ⋊ C3
HallC11⋊(D67⋊C3) ⋊ C5
HallC11⋊C5×C67 ⋊ C2×C3
HallC11×C67⋊C3 ⋊ C2×C5
HallD737 ⋊ C3×C5
HallC67⋊C3 ⋊ AGL(1,𝔽11)
SylowC67 ⋊ C3×AGL(1,𝔽11)
HallC11⋊C5 ⋊ D67⋊C3
SylowC11 ⋊ C5×D67⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C67C2×C3×C5
LCSG ▷ C11×C67
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 737

Polycyclic presentation:

2,3,5,11,67|d^a=d^10,e^a=e^66,e^b=e^37,d^c=d^4

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22110, 48);