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C5×C29×C5⋊AGL(1,𝔽7) #44478589

order30450
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC5×C29×C5⋊AGL(1,𝔽7)
unambiguous semidirect productC5⋊(C5×C29×AGL(1,𝔽7))
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×D5×C29)
unambiguous semidirect productD35⋊(C3×C5×C29)
unambiguous semidirect product(C5×D35)⋊(C3×C29)
unambiguous semidirect product(C29×D35)⋊(C3×C5)
unambiguous semidirect product(C5×C29×D35)⋊C3

Splittings

Fitting, socle, HallC52×C7×C29 ⋊ C2×C3
derivedC5×C7 ⋊ C2×C3×C5×C29
HallC52×ΓL(1,𝔽8)×C29 ⋊ C2
HallC5×C29×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
HallC52×C7 ⋊ C2×C3×C29
SylowC52 ⋊ C29×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C5×D5×C29
SylowC7 ⋊ C3×C5×D5×C29

Subgroups

subgroupG/H
center, hypercenterC5×C29C5⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7C2×C3×C5×C29
FrattiniC1G
Fitting, socleC52×C7×C29C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C5×C29

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2030

Conjugacy classes & character table

2465 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 73);