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C71×C7⋊AGL(1,𝔽5) #23755486

order9940
isoclinismisoclinic class of C7⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C71 · Schur multiplier (H2) = C1

Aliases

direct productC71×C7⋊AGL(1,𝔽5)
unambiguous semidirect productC7⋊(AGL(1,𝔽5)×C71)

Splittings

Fitting, socle, HallC5×C7×C71 ⋊ C4
derived, HallC5×C7 ⋊ C4×C71
HallC7×C71 ⋊ AGL(1,𝔽5)
HallC5×C71 ⋊ Dic7
SylowC7 ⋊ AGL(1,𝔽5)×C71
SylowC5 ⋊ Dic7×C71

Subgroups

subgroupG/H
center, hypercenterC71C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C4×C71
FrattiniC1G
Fitting, socleC5×C7×C71C4
prime radicalC7×D5×C71C2
cosocleC7×D5C2×C71
LCSG ▷ C5×C7
UCSC1 ◁ C71

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1207 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC71×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C3×C71×C7⋊AGL(1,𝔽5), C71×C3⋊(C7⋊AGL(1,𝔽5))
maximal normal subgroup ofC71×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C3×C71×C7⋊AGL(1,𝔽5)
maximal quotient ofC3×C71×C7⋊AGL(1,𝔽5), C71×C3⋊(C7⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9940, 37);