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C2×C52×C17⋊AGL(1,𝔽7) #49087852

order35700
automorphism?
homologyAbelianization (H1) = C22×C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C52×C17⋊AGL(1,𝔽7)
unambiguous semidirect product(C2×C17)⋊(C52×AGL(1,𝔽7))
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C52×D17)
unambiguous semidirect product(C2×D119)⋊(C3×C52)
unambiguous semidirect product(C2×C5×D119)⋊(C3×C5)

Splittings

Fitting, socleC2×C52×C7×C17 ⋊ C2×C3
derived, HallC7×C17 ⋊ C22×C3×C52
HallC2×C52×D119 ⋊ C3
HallC52×C17×ΓL(1,𝔽8) ⋊ C22
HallC52×C7×C17 ⋊ C22×C3
HallC52×ΓL(1,𝔽8) ⋊ C2×D17
HallC2×D119 ⋊ C3×C52
HallC52×C17 ⋊ C2×AGL(1,𝔽7)
HallC17×ΓL(1,𝔽8) ⋊ C22×C52
HallC52×C7 ⋊ C2×C3×D17
HallΓL(1,𝔽8) ⋊ C2×C52×D17
SylowC17 ⋊ C2×C52×AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×C52×D17

Subgroups

subgroupG/H
center, hypercenterC2×C52C17⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C17C22×C3×C52
FrattiniC1G
Fitting, socleC2×C52×C7×C17C2×C3
LCSG ▷ C7×C17
UCSC1 ◁ C2×C52

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5950

Conjugacy classes & character table

2350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 326);