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C3×C17×C11⋊AGL(1,𝔽5) #26014377

order11220
isoclinismisoclinic class of C11⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×C11⋊AGL(1,𝔽5)
unambiguous semidirect productC11⋊(C3×C17×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC3×C5×C11×C17 ⋊ C4
derived, HallC5×C11 ⋊ C3×C4×C17
HallC5×C11×C17 ⋊ C3×C4
HallC3×C11×C17 ⋊ AGL(1,𝔽5)
HallC3×C5×C17 ⋊ Dic11
HallC11×C17 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C11 ⋊ C4×C17
HallC5×C17 ⋊ C3×Dic11
HallC3×C11 ⋊ C17×AGL(1,𝔽5)
HallC3×C5 ⋊ C17×Dic11
SylowC11 ⋊ C3×C17×AGL(1,𝔽5)
SylowC5 ⋊ C3×C17×Dic11

Subgroups

subgroupG/H
center, hypercenterC3×C17C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C3×C4×C17
FrattiniC1G
Fitting, socleC3×C5×C11×C17C4
prime radicalC3×D5×C11×C17C2
cosocleD5×C11C2×C3×C17
LCSG ▷ C5×C11
UCSC1 ◁ C3×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1275 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C17×C11⋊AGL(1,𝔽5), C32×C17×C11⋊AGL(1,𝔽5), C3×C17×C3⋊(C11⋊AGL(1,𝔽5))
maximal normal subgroup ofC9×C17×C11⋊AGL(1,𝔽5), C32×C17×C11⋊AGL(1,𝔽5)
maximal quotient ofC9×C17×C11⋊AGL(1,𝔽5), C32×C17×C11⋊AGL(1,𝔽5), C3×C17×C3⋊(C11⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 53);