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C121×C3⋊ΓL(1,𝔽16) #36344727

order21780
isoclinismisoclinic class of C3⋊ΓL(1,𝔽16)
automorphism?
homologyAbelianization (H1) = C4×C121 · Schur multiplier (H2) = C3

Aliases

direct productC121×C3⋊ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(ΓL(1,𝔽16)×C121)

Splittings

Fitting, HallC32×C5×C121 ⋊ C4
derived, HallC32×C5 ⋊ C4×C121
HallC32×C121 ⋊ AGL(1,𝔽5)
HallC5×C121 ⋊ C3⋊Dic3
SylowC32 ⋊ AGL(1,𝔽5)×C121
SylowC5 ⋊ C3⋊Dic3×C121

Subgroups

subgroupG/H
center, hypercenterC121C3⋊ΓL(1,𝔽16)
commutator, hypocenterC32×C5C4×C121
FrattiniC11C11×C3⋊ΓL(1,𝔽16)
FittingC32×C5×C121C4
socleC32×C5×C11C4×C11
prime radical, cosocleC32×D5×C11C2×C11
LCSG ▷ C32×C5
UCSC1 ◁ C121

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2541 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 76);