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C11×C3⋊(C11⋊AGL(1,𝔽5)) #20300100

order7260
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊(C11⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C11×C11⋊AGL(1,𝔽5))
unambiguous semidirect productC11⋊(C11×ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC3×C5×C112 ⋊ C4
derivedC3×C5×C11 ⋊ C4×C11
HallC5×C112 ⋊ Dic3
HallC3×C112 ⋊ AGL(1,𝔽5)
SylowC112 ⋊ ΓL(1,𝔽16)
HallC3×C5 ⋊ C11×Dic11
SylowC5 ⋊ C11×Dic33
SylowC3 ⋊ C11×C11⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C11⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C11C4×C11
FrattiniC1G
Fitting, socleC3×C5×C112C4
LCSG ▷ C3×C5×C11
UCSC1 ◁ C11

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

759 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#36344868, C11×C9⋊(C11⋊AGL(1,𝔽5)), C3⋊#20300037, …
maximal normal subgroup ofC3×C11×C3⋊(C11⋊AGL(1,𝔽5)), C11×C3⋊((C11⋊C5)⋊AGL(1,𝔽5)), C11⋊C5×C3⋊(C11⋊AGL(1,𝔽5)), …
maximal quotient ofC11×C9⋊(C11⋊AGL(1,𝔽5)), C3×C11×C3⋊(C11⋊AGL(1,𝔽5)), C11×C3⋊(C3⋊(C11⋊AGL(1,𝔽5))), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 200);