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C11×#11763984 #26046464

order12012
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#11763984

Splittings

Fitting, socle, HallC7×C11×C13 ⋊ C3×C4
derived, HallC7×C13 ⋊ C3×C4×C11
HallC11×C7⋊#261 ⋊ C3
HallC11×#63271 ⋊ C4
HallC7⋊#261 ⋊ C3×C11
Hall#63271 ⋊ C4×C11
HallC11×C13 ⋊ ΓL(1,𝔽8)⋊C4
HallC7×C11 ⋊ AGL(1,𝔽13)
SylowC13 ⋊ C11×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C11×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC11#11763984
commutator, hypocenterC7×C13C3×C4×C11
FrattiniC1G
Fitting, socleC7×C11×C13C3×C4
prime radicalC11×#10587717C2
cosocleC7×D13C2×C3×C11
LCSG ▷ C7×C13
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 54);