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(C11⋊C5)⋊(D109⋊C3) #49112596

order35970
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C11⋊C5)⋊(D109⋊C3)
unambiguous semidirect product(C109⋊C3)⋊AGL(1,𝔽11)
unambiguous semidirect product(C11⋊(D109⋊C3))⋊C5
unambiguous semidirect product((C11⋊C5)⋊D109)⋊C3

Splittings

Fitting, socle, derived, HallC11×C109 ⋊ C2×C3×C5
HallC11⋊C5×C109⋊C3 ⋊ C2
Hall(C11⋊C5)⋊D109 ⋊ C3
HallC11⋊(D109⋊C3) ⋊ C5
HallC11⋊C5×C109 ⋊ C2×C3
HallC11×C109⋊C3 ⋊ C2×C5
HallD1199 ⋊ C3×C5
HallC109⋊C3 ⋊ AGL(1,𝔽11)
SylowC109 ⋊ C3×AGL(1,𝔽11)
HallC11⋊C5 ⋊ D109⋊C3
SylowC11 ⋊ C5×D109⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C109C2×C3×C5
LCSG ▷ C11×C109
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1199

Polycyclic presentation:

2,3,5,11,109|d^a=d^10,e^a=e^108,e^b=e^63,d^c=d^4

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35970, 36);