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C7×C11×C3⋊ΓL(1,𝔽16) #28357698

order13860
isoclinismisoclinic class of C3⋊ΓL(1,𝔽16)
automorphism?
homologyAbelianization (H1) = C4×C7×C11 · Schur multiplier (H2) = C3

Aliases

direct productC7×C11×C3⋊ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(C7×C11×ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C4
derived, HallC32×C5 ⋊ C4×C7×C11
HallC32×C7×C11 ⋊ AGL(1,𝔽5)
HallC32×C5×C11 ⋊ C4×C7
HallC5×C7×C11 ⋊ C3⋊Dic3
HallC32×C5×C7 ⋊ C4×C11
HallC32×C11 ⋊ C7×AGL(1,𝔽5)
HallC32×C7 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ C7×C3⋊Dic3
HallC5×C7 ⋊ C11×C3⋊Dic3
SylowC32 ⋊ C7×C11×AGL(1,𝔽5)
SylowC5 ⋊ C7×C11×C3⋊Dic3

Subgroups

subgroupG/H
center, hypercenterC7×C11C3⋊ΓL(1,𝔽16)
commutator, hypocenterC32×C5C4×C7×C11
FrattiniC1G
Fitting, socleC32×C5×C7×C11C4
prime radicalC32×C7×D5×C11C2
cosocleC32×D5C2×C7×C11
LCSG ▷ C32×C5
UCSC1 ◁ C7×C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3465

Conjugacy classes & character table

1617 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 365);