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C13×C3⋊(C11⋊AGL(1,𝔽5)) #22575151

order8580
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊(C11⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C13×C11⋊AGL(1,𝔽5))
unambiguous semidirect productC11⋊(C13×ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC3×C5×C11×C13 ⋊ C4
derived, HallC3×C5×C11 ⋊ C4×C13
HallC5×C11×C13 ⋊ Dic3
HallC3×C11×C13 ⋊ AGL(1,𝔽5)
HallC3×C5×C13 ⋊ Dic11
HallC11×C13 ⋊ ΓL(1,𝔽16)
HallC5×C13 ⋊ Dic33
HallC5×C11 ⋊ Dic3×C13
HallC3×C13 ⋊ C11⋊AGL(1,𝔽5)
HallC3×C11 ⋊ C13×AGL(1,𝔽5)
HallC3×C5 ⋊ C13×Dic11
SylowC11 ⋊ C13×ΓL(1,𝔽16)
SylowC5 ⋊ C13×Dic33
SylowC3 ⋊ C13×C11⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC13C3⋊(C11⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C11C4×C13
FrattiniC1G
Fitting, socleC3×C5×C11×C13C4
LCSG ▷ C3×C5×C11
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

897 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×C9⋊(C11⋊AGL(1,𝔽5)), C13⋊C3×C3⋊(C11⋊AGL(1,𝔽5)), C3×C13×C3⋊(C11⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC13⋊C3×C3⋊(C11⋊AGL(1,𝔽5)), C3×C13×C3⋊(C11⋊AGL(1,𝔽5))
maximal quotient ofC13×C9⋊(C11⋊AGL(1,𝔽5)), C3×C13×C3⋊(C11⋊AGL(1,𝔽5)), C13×C3⋊(C3⋊(C11⋊AGL(1,𝔽5)))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 123);