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C52×C29×AGL(1,𝔽7) #44478586

order30450
automorphism?
homologyAbelianization (H1) = C2×C3×C52×C29 · Schur multiplier (H2) = C5

Aliases

direct productC52×C29×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C52×C29)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C52×C29)
unambiguous semidirect product(C5×D7)⋊(C3×C5×C29)
unambiguous semidirect product(D7×C29)⋊(C3×C52)
unambiguous semidirect product(C5×D7×C29)⋊(C3×C5)

Splittings

Fitting, socle, HallC52×C7×C29 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C52×C29
HallC52×ΓL(1,𝔽8)×C29 ⋊ C2
HallC52×D7×C29 ⋊ C3
HallΓL(1,𝔽8)×C29 ⋊ C2×C52
HallC52×ΓL(1,𝔽8) ⋊ C2×C29
HallD7×C29 ⋊ C3×C52
HallC52×D7 ⋊ C3×C29
HallC7×C29 ⋊ C2×C3×C52
HallC52×C7 ⋊ C2×C3×C29
HallΓL(1,𝔽8) ⋊ C2×C52×C29
HallD7 ⋊ C3×C52×C29

Subgroups

subgroupG/H
center, hypercenterC52×C29AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C3×C52×C29
FrattiniC1G
Fitting, socleC52×C7×C29C2×C3
LCSG ▷ C7
UCSC1 ◁ C52×C29

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5075

Conjugacy classes & character table

5075 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 70);