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(C11⋊C5)⋊#3866 #22550778

order8140
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC11×C37C4×C5
LCSG ▷ C11×C37
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

85 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C11⋊C5)⋊(#3866⋊C3), C3×(C11⋊C5)⋊#3866, C3⋊((C11⋊C5)⋊#3866)
maximal normal subgroup of(C11⋊C5)⋊(#3866⋊C3), C3×(C11⋊C5)⋊#3866
maximal quotient ofC3×(C11⋊C5)⋊#3866, C3⋊((C11⋊C5)⋊#3866)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8140, 14);