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C5×C29×AGL(1,𝔽7) #20259041

order6090
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC5×C29×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C5×C29)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C5×C29)
unambiguous semidirect product(C5×D7)⋊(C3×C29)
unambiguous semidirect product(D7×C29)⋊(C3×C5)
unambiguous semidirect product(C5×D7×C29)⋊C3

Splittings

Fitting, socle, HallC5×C7×C29 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C5×C29
HallC5×ΓL(1,𝔽8)×C29 ⋊ C2
HallC5×D7×C29 ⋊ C3
HallΓL(1,𝔽8)×C29 ⋊ C2×C5
HallD7×C29 ⋊ C3×C5
HallC7×C29 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8) ⋊ C2×C29
HallC5×D7 ⋊ C3×C29
HallC5×C7 ⋊ C2×C3×C29
HallΓL(1,𝔽8) ⋊ C2×C5×C29
HallD7 ⋊ C3×C5×C29

Subgroups

subgroupG/H
center, hypercenterC5×C29AGL(1,𝔽7)
commutator, hypocenterC7C2×C3×C5×C29
FrattiniC1G
Fitting, socleC5×C7×C29C2×C3
LCSG ▷ C7
UCSC1 ◁ C5×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1015 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×C29×AGL(1,𝔽7), C5×C29×C3⋊AGL(1,𝔽7), C25×C29×AGL(1,𝔽7), …
maximal normal subgroup ofC3×C5×C29×AGL(1,𝔽7), C25×C29×AGL(1,𝔽7), C52×C29×AGL(1,𝔽7)
maximal quotient ofC5×C29×D7⋊C9, C3×C5×C29×AGL(1,𝔽7), C5×C29×C3⋊AGL(1,𝔽7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6090, 27);