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C2×C5×C7⋊AGL(1,𝔽5) #13063847

order1400
isoclinismisoclinic class of C7⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7⋊AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C5×Dic7)
unambiguous semidirect product(C2×C7)⋊(C5×AGL(1,𝔽5))

Splittings

Fitting, socleC2×C52×C7 ⋊ C4
derivedC5×C7 ⋊ C2×C4×C5
HallC52×C7 ⋊ C2×C4
SylowC52 ⋊ C2×Dic7
SylowC7 ⋊ C2×C5×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC2×C5C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C2×C4×C5
FrattiniC1G
Fitting, socleC2×C52×C7C4
prime radicalC2×C5×C7×D5C2
cosocleC7×D5C22×C5
LCSG ▷ C5×C7
UCSC1 ◁ C2×C5

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 280

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C2×C5×D7×AGL(1,𝔽5), C4×C5×C7⋊AGL(1,𝔽5), …
maximal normal subgroup ofC2×C5×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C2×C5×D7×AGL(1,𝔽5), C4×C5×C7⋊AGL(1,𝔽5), …
maximal quotient ofC4×C5×C7⋊AGL(1,𝔽5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1400, 136);