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C13×AGL(1,𝔽5)×C13⋊C3 #23778452

order10140
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×AGL(1,𝔽5)×C13⋊C3
unambiguous semidirect product(C13×AGL(1,𝔽5))⋊(C3×C13)

Splittings

Fitting, socle, HallC5×C132 ⋊ C3×C4
derivedC5×C13 ⋊ C3×C4×C13
HallC132×AGL(1,𝔽5) ⋊ C3
HallC5×C13×C13⋊C3 ⋊ C4
SylowC132 ⋊ C3×AGL(1,𝔽5)
SylowC5 ⋊ C4×C13×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC13AGL(1,𝔽5)×C13⋊C3
commutator, hypocenterC5×C13C3×C4×C13
FrattiniC1G
Fitting, socleC5×C132C3×C4
prime radicalD5×C13×C13⋊C3C2
cosocleD5×C13C2×C3×C13
LCSG ▷ C5×C13
UCSC1 ◁ C13

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

455 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×C13⋊C32, C3×C13×AGL(1,𝔽5)×C13⋊C3, C13×C13⋊C3×ΓL(1,𝔽16)
maximal normal subgroup ofAGL(1,𝔽5)×C13⋊C32, C3×C13×AGL(1,𝔽5)×C13⋊C3
maximal quotient ofC13×AGL(1,𝔽5)×C13⋊C9, C3×C13×AGL(1,𝔽5)×C13⋊C3, C13×C13⋊C3×ΓL(1,𝔽16)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 110);