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C8×C5⋊AGL(1,𝔽7) #13132052

order1680
isoclinismisoclinic class of C5⋊AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2

Aliases

direct productC8×C5⋊AGL(1,𝔽7)
unambiguous semidirect product(C8×D35)⋊C3

Splittings

FittingC5×C7×C8 ⋊ C2×C3
derived, HallC5×C7 ⋊ C2×C3×C8
HallC8×D35 ⋊ C3
HallC5×ΓL(1,𝔽8) ⋊ C2×C8
HallΓL(1,𝔽8) ⋊ C8×D5
SylowC7 ⋊ C3×C8×D5
SylowC5 ⋊ C8×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, hypercenterC8C5⋊AGL(1,𝔽7)
commutator, hypocenterC5×C7C2×C3×C8
FrattiniC4C2×C5⋊AGL(1,𝔽7)
FittingC5×C7×C8C2×C3
socleC2×C5×C7C2×C3×C4
prime radicalC2×C5⋊AGL(1,𝔽7)C4
cosocleC4×C5×C7C22×C3
LCSG ▷ C5×C7
UCSC1 ◁ C8

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 280

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽9)×C5⋊AGL(1,𝔽7), C8×D5×AGL(1,𝔽7), M16×C5⋊AGL(1,𝔽7), …
maximal normal subgroup ofC8×D5×AGL(1,𝔽7), M16×C5⋊AGL(1,𝔽7), #72217888, …
maximal quotient ofAGL(1,𝔽9)×C5⋊AGL(1,𝔽7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1680, 72);