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C2×C5×C5⋊AGL(1,𝔽7) #14523616

order2100
isoclinismisoclinic class of C5⋊AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C5⋊AGL(1,𝔽7)
unambiguous semidirect product(C2×C5)⋊(C5×AGL(1,𝔽7))
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C5×D5)
unambiguous semidirect product(C2×D35)⋊(C3×C5)
unambiguous semidirect product(C2×C5×D35)⋊C3

Splittings

Fitting, socleC2×C52×C7 ⋊ C2×C3
derivedC5×C7 ⋊ C22×C3×C5
HallC2×C5×D35 ⋊ C3
HallC52×ΓL(1,𝔽8) ⋊ C22
HallC52×C7 ⋊ C22×C3
SylowC52 ⋊ C2×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C2×C5×D5
SylowC7 ⋊ C2×C3×C5×D5

Subgroups

subgroupG/H
center, hypercenterC2×C5C5⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7C22×C3×C5
FrattiniC1G
Fitting, socleC2×C52×C7C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 140

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×C5⋊(D49⋊C3), C5×#64423⋊D5, C5×#64422⋊D5, …
maximal normal subgroup ofC2×C5×C7×C5⋊AGL(1,𝔽7), C2×C5×C11×C5⋊AGL(1,𝔽7), C2×C5×C13×C5⋊AGL(1,𝔽7), …
maximal quotient ofC2×C5×C5⋊(D49⋊C3), C5×#64423⋊D5, C5×#64422⋊D5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 96);