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C29×C5⋊(C5⋊AGL(1,𝔽7)) #44478593

order30450
automorphism?
homologyAbelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C5

Aliases

direct productC29×C5⋊(C5⋊AGL(1,𝔽7))
unambiguous semidirect productC5⋊(C29×C5⋊AGL(1,𝔽7))
unambiguous semidirect productΓL(1,𝔽8)⋊(C29×C5⋊D5)

Splittings

Fitting, socle, HallC52×C7×C29 ⋊ C2×C3
derived, HallC52×C7 ⋊ C2×C3×C29
HallC52×ΓL(1,𝔽8)×C29 ⋊ C2
HallC29×C5⋊D35 ⋊ C3
HallC52×C29 ⋊ AGL(1,𝔽7)
HallΓL(1,𝔽8)×C29 ⋊ C5⋊D5
HallC52×ΓL(1,𝔽8) ⋊ C2×C29
HallC5⋊D35 ⋊ C3×C29
HallC7×C29 ⋊ C3×C5⋊D5
SylowC52 ⋊ C29×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C29×C5⋊D5
SylowC7 ⋊ C3×C29×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC29C5⋊(C5⋊AGL(1,𝔽7))
commutator, cosocle, hypocenterC52×C7C2×C3×C29
FrattiniC1G
Fitting, socleC52×C7×C29C2×C3
LCSG ▷ C52×C7
UCSC1 ◁ C29

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5075

Conjugacy classes & character table

1943 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 77);