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C11×C17×ΓL(1,𝔽16) #26014397

order11220
isoclinismisoclinic class of ΓL(1,𝔽16)
automorphism?
homologyAbelianization (H1) = C4×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC11×C17×ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(C11×C17×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC3×C5×C11×C17 ⋊ C4
derived, HallC3×C5 ⋊ C4×C11×C17
HallC5×C11×C17 ⋊ Dic3
HallC3×C11×C17 ⋊ AGL(1,𝔽5)
HallC3×C5×C17 ⋊ C4×C11
HallC3×C5×C11 ⋊ C4×C17
HallC5×C17 ⋊ C11×Dic3
HallC5×C11 ⋊ Dic3×C17
HallC3×C17 ⋊ C11×AGL(1,𝔽5)
HallC3×C11 ⋊ C17×AGL(1,𝔽5)
SylowC5 ⋊ C11×Dic3×C17
SylowC3 ⋊ C11×C17×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC11×C17ΓL(1,𝔽16)
commutator, hypocenterC3×C5C4×C11×C17
FrattiniC1G
Fitting, socleC3×C5×C11×C17C4
prime radicalC3×D5×C11×C17C2
cosocleC3×D5C2×C11×C17
LCSG ▷ C3×C5
UCSC1 ◁ C11×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1683 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×C17×C9⋊AGL(1,𝔽5), C3×C11×C17×ΓL(1,𝔽16), C11×C17×C3⋊ΓL(1,𝔽16)
maximal normal subgroup ofC3×C11×C17×ΓL(1,𝔽16)
maximal quotient ofC11×C17×C9⋊AGL(1,𝔽5), C3×C11×C17×ΓL(1,𝔽16), C11×C17×C3⋊ΓL(1,𝔽16)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 73);