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C7×C59⋊AGL(1,𝔽5) #22551893

order8260
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C59⋊AGL(1,𝔽5)
unambiguous semidirect productC59⋊(C7×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC5×C7×C59 ⋊ C4
derived, HallC5×C59 ⋊ C4×C7
HallC7×C59 ⋊ AGL(1,𝔽5)
SylowC59 ⋊ C7×AGL(1,𝔽5)
HallC5×C7 ⋊ Dic59
SylowC5 ⋊ C7×Dic59

Subgroups

subgroupG/H
center, hypercenterC7C59⋊AGL(1,𝔽5)
commutator, hypocenterC5×C59C4×C7
FrattiniC1G
Fitting, socleC5×C7×C59C4
LCSG ▷ C5×C59
UCSC1 ◁ C7

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

847 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)×C59⋊AGL(1,𝔽5), C3×C7×C59⋊AGL(1,𝔽5), C7×C3⋊(C59⋊AGL(1,𝔽5))
maximal normal subgroup ofΓL(1,𝔽8)×C59⋊AGL(1,𝔽5), C3×C7×C59⋊AGL(1,𝔽5)
maximal quotient ofC3×C7×C59⋊AGL(1,𝔽5), C7×C3⋊(C59⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8260, 12);