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C11⋊(#10625192⋊C3) #37567545

order24420
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC11⋊(#10625192⋊C3)
unambiguous semidirect product(C11⋊#10625192)⋊C3

Splittings

Fitting, socle, derived, HallC5×C11×C37 ⋊ C3×C4
HallC11⋊#10625192 ⋊ C3
HallC5×C11×C37⋊C3 ⋊ C4
HallC11×C37⋊C3 ⋊ AGL(1,𝔽5)
HallC5×C37⋊C3 ⋊ Dic11
HallC11×C37 ⋊ C3×AGL(1,𝔽5)
HallC5×C37 ⋊ C3×Dic11
HallC37⋊C3 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C11 ⋊ #3866⋊C3
SylowC37 ⋊ C3×C11⋊AGL(1,𝔽5)
SylowC11 ⋊ #10625192⋊C3
SylowC5 ⋊ C11⋊(#3866⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C11×C37C3×C4
prime radicalC11×C5⋊(D37⋊C3)C2
cosocleC11×D185C2×C3
LCSG ▷ C5×C11×C37
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2035

Polycyclic presentation:

2,3,2,5,11,37|a^2=c,d^a=d^2,e^a=e^10,f^a=f^6,f^b=f^26,d^c=d^4,f^c=f^36

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 66);