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C52×ΓL(1,𝔽8)⋊D29 #44478587

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

Aliases

direct productC52×ΓL(1,𝔽8)⋊D29
unambiguous semidirect productΓL(1,𝔽8)⋊(C52×D29)
unambiguous semidirect productC29⋊(C52×AGL(1,𝔽7))
unambiguous semidirect productD203⋊(C3×C52)
unambiguous semidirect product(C5×D203)⋊(C3×C5)

Splittings

Fitting, socle, HallC52×C7×C29 ⋊ C2×C3
derived, HallC7×C29 ⋊ C2×C3×C52
HallC52×ΓL(1,𝔽8)×C29 ⋊ C2
HallC52×D203 ⋊ C3
HallC52×C29 ⋊ AGL(1,𝔽7)
HallΓL(1,𝔽8)×C29 ⋊ C2×C52
HallC52×ΓL(1,𝔽8) ⋊ D29
HallD203 ⋊ C3×C52
HallC52×C7 ⋊ C3×D29
SylowC29 ⋊ C52×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C52×D29
SylowC7 ⋊ C3×C52×D29

Subgroups

subgroupG/H
center, hypercenterC52ΓL(1,𝔽8)⋊D29
commutator, cosocle, hypocenterC7×C29C2×C3×C52
FrattiniC1G
Fitting, socleC52×C7×C29C2×C3
LCSG ▷ C7×C29
UCSC1 ◁ C52

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5075

Conjugacy classes & character table

1925 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 71);