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C11×AGL(1,𝔽5)×C13⋊C3 #22575092

order8580
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×AGL(1,𝔽5)×C13⋊C3
unambiguous semidirect product(C13×AGL(1,𝔽5))⋊(C3×C11)
unambiguous semidirect product(C11×C13×AGL(1,𝔽5))⋊C3

Splittings

Fitting, socle, HallC5×C11×C13 ⋊ C3×C4
derived, HallC5×C13 ⋊ C3×C4×C11
HallC11×C13×AGL(1,𝔽5) ⋊ C3
HallC5×C11×C13⋊C3 ⋊ C4
HallC13×AGL(1,𝔽5) ⋊ C3×C11
HallC5×C13⋊C3 ⋊ C4×C11
HallC11×C13 ⋊ C3×AGL(1,𝔽5)
HallC5×C11 ⋊ C4×C13⋊C3
SylowC13 ⋊ C3×C11×AGL(1,𝔽5)
SylowC5 ⋊ C4×C11×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC11AGL(1,𝔽5)×C13⋊C3
commutator, hypocenterC5×C13C3×C4×C11
FrattiniC1G
Fitting, socleC5×C11×C13C3×C4
LCSG ▷ C5×C13
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

385 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11×AGL(1,𝔽5)×C13⋊C3, C11×C13⋊C3×ΓL(1,𝔽16)
maximal normal subgroup ofC3×C11×AGL(1,𝔽5)×C13⋊C3
maximal quotient ofC11×AGL(1,𝔽5)×C13⋊C9, C3×C11×AGL(1,𝔽5)×C13⋊C3, C11×C13⋊C3×ΓL(1,𝔽16)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 64);