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C11×C13×ΓL(1,𝔽16) #22575147

order8580
isoclinismisoclinic class of ΓL(1,𝔽16)
automorphism?
homologyAbelianization (H1) = C4×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC11×C13×ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(C11×C13×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC3×C5×C11×C13 ⋊ C4
derived, HallC3×C5 ⋊ C4×C11×C13
HallC5×C11×C13 ⋊ Dic3
HallC3×C11×C13 ⋊ AGL(1,𝔽5)
HallC3×C5×C13 ⋊ C4×C11
HallC3×C5×C11 ⋊ C4×C13
HallC5×C13 ⋊ C11×Dic3
HallC5×C11 ⋊ Dic3×C13
HallC3×C13 ⋊ C11×AGL(1,𝔽5)
HallC3×C11 ⋊ C13×AGL(1,𝔽5)
SylowC5 ⋊ C11×Dic3×C13
SylowC3 ⋊ C11×C13×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC11×C13ΓL(1,𝔽16)
commutator, hypocenterC3×C5C4×C11×C13
FrattiniC1G
Fitting, socleC3×C5×C11×C13C4
LCSG ▷ C3×C5
UCSC1 ◁ C11×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1287 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×C13×C9⋊AGL(1,𝔽5), C11×C13⋊C3×ΓL(1,𝔽16), C3×C11×C13×ΓL(1,𝔽16), …
maximal normal subgroup ofC11×C13⋊C3×ΓL(1,𝔽16), C3×C11×C13×ΓL(1,𝔽16)
maximal quotient ofC11×C13×C9⋊AGL(1,𝔽5), C3×C11×C13×ΓL(1,𝔽16), C11×C13×C3⋊ΓL(1,𝔽16)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 119);