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C11⋊#11763984 #26046482

order12012
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC11⋊#11763984

Splittings

Fitting, socle, derived, HallC7×C11×C13 ⋊ C3×C4
HallC7⋊(C11⋊#261) ⋊ C3
HallC11×#63271 ⋊ C4
Hall#63271 ⋊ Dic11
HallC11×C13 ⋊ ΓL(1,𝔽8)⋊C4
HallC7×C13 ⋊ C3×Dic11
HallC7×C11 ⋊ AGL(1,𝔽13)
SylowC13 ⋊ C11⋊(ΓL(1,𝔽8)⋊C4)
SylowC11 ⋊ #11763984
SylowC7 ⋊ C11⋊AGL(1,𝔽13)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC7×C11×C13C3×C4
prime radicalC11×#10587717C2
cosocleC7×C11×D13C2×C3
LCSG ▷ C7×C11×C13
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,2,7,11,13|a^2=c,d^a=d^6,e^a=e^10,f^a=f^5,d^b=d^2,f^b=f^9,f^c=f^12

Conjugacy classes & character table

141 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽13)), C3×C11⋊#11763984, C3⋊(C11⋊#11763984)
maximal normal subgroup ofC11⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽13)), C3×C11⋊#11763984
maximal quotient ofC11⋊#15692591, C3×C11⋊#11763984, C3⋊(C11⋊#11763984)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 72);