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C29×C3⋊(C7⋊AGL(1,𝔽5)) #27131784

order12180
isoclinismisoclinic class of C3⋊(C7⋊AGL(1,𝔽5))
automorphism?
homologyAbelianization (H1) = C4×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×C3⋊(C7⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C29×C7⋊AGL(1,𝔽5))
unambiguous semidirect productC7⋊(C29×ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC3×C5×C7×C29 ⋊ C4
derived, HallC3×C5×C7 ⋊ C4×C29
HallC5×C7×C29 ⋊ Dic3
HallC3×C7×C29 ⋊ AGL(1,𝔽5)
HallC3×C5×C29 ⋊ Dic7
HallC7×C29 ⋊ ΓL(1,𝔽16)
HallC5×C29 ⋊ Dic21
HallC3×C29 ⋊ C7⋊AGL(1,𝔽5)
HallC5×C7 ⋊ Dic3×C29
HallC3×C7 ⋊ AGL(1,𝔽5)×C29
HallC3×C5 ⋊ Dic7×C29
SylowC7 ⋊ C29×ΓL(1,𝔽16)
SylowC5 ⋊ C29×Dic21
SylowC3 ⋊ C29×C7⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC29C3⋊(C7⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C7C4×C29
FrattiniC1G
Fitting, socleC3×C5×C7×C29C4
LCSG ▷ C3×C5×C7
UCSC1 ◁ C29

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1305 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC29×C7⋊(C9⋊AGL(1,𝔽5)), C29×C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5)), C3×C29×C3⋊(C7⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC29×C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5)), C3×C29×C3⋊(C7⋊AGL(1,𝔽5))
maximal quotient ofC29×C7⋊(C9⋊AGL(1,𝔽5)), C3×C29×C3⋊(C7⋊AGL(1,𝔽5)), C29×C3⋊(C3⋊(C7⋊AGL(1,𝔽5)))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 119);