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(C11⋊C5)⋊(#3866⋊C3) #37567517

order24420
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C11⋊C5)⋊(#3866⋊C3)
unambiguous semidirect product(C11⋊(#3866⋊C3))⋊C5
unambiguous semidirect product((C11⋊C5)⋊#3866)⋊C3

Splittings

Fitting, socle, derived, HallC11×C37 ⋊ C3×C4×C5
Hall(C11⋊C5)⋊#3866 ⋊ C3
HallC11⋊C5×C37⋊C3 ⋊ C4
HallC11⋊(#3866⋊C3) ⋊ C5
HallC37×C11⋊C5 ⋊ C3×C4
HallC11⋊#3866 ⋊ C3×C5
HallC11×C37⋊C3 ⋊ C4×C5
HallC37⋊C3 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ #3866⋊C3
SylowC37 ⋊ C3×Dic11⋊C5
SylowC11 ⋊ C5×#3866⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC11×C37C3×C4×C5
prime radicalC11⋊C5×D37⋊C3C2
cosocleC11×D37C2×C3×C5
LCSG ▷ C11×C37
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 407

Polycyclic presentation:

2,3,5,2,11,37|a^2=d,e^a=e^10,f^a=f^31,f^b=f^26,e^c=e^4,f^d=f^36

Conjugacy classes & character table

87 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 38);