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C59×C7⋊AGL(1,𝔽5) #22551894

order8260
isoclinismisoclinic class of C7⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C59 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC5×C7×C59 ⋊ C4
derived, HallC5×C7 ⋊ C4×C59
HallC7×C59 ⋊ AGL(1,𝔽5)
HallC5×C59 ⋊ Dic7
SylowC7 ⋊ AGL(1,𝔽5)×C59
SylowC5 ⋊ Dic7×C59

Subgroups

subgroupG/H
center, hypercenterC59C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C4×C59
FrattiniC1G
Fitting, socleC5×C7×C59C4
LCSG ▷ C5×C7
UCSC1 ◁ C59

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1003 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC59×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C3×C59×C7⋊AGL(1,𝔽5), C59×C3⋊(C7⋊AGL(1,𝔽5))
maximal normal subgroup ofC59×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C3×C59×C7⋊AGL(1,𝔽5)
maximal quotient ofC3×C59×C7⋊AGL(1,𝔽5), C59×C3⋊(C7⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8260, 13);