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C2×C17×C5⋊(C5⋊AGL(1,𝔽7)) #49087858

order35700
automorphism?
homologyAbelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C17×C5⋊(C5⋊AGL(1,𝔽7))
unambiguous semidirect product(C2×C5)⋊(C17×C5⋊AGL(1,𝔽7))
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C17×C5⋊D5)

Splittings

Fitting, socleC2×C52×C7×C17 ⋊ C2×C3
derived, HallC52×C7 ⋊ C22×C3×C17
HallC2×C17×C5⋊D35 ⋊ C3
HallC52×C17×ΓL(1,𝔽8) ⋊ C22
HallC52×C7×C17 ⋊ C22×C3
HallC2×C5⋊D35 ⋊ C3×C17
HallC52×ΓL(1,𝔽8) ⋊ C22×C17
HallC52×C17 ⋊ C2×AGL(1,𝔽7)
HallC17×ΓL(1,𝔽8) ⋊ C2×C5⋊D5
HallC7×C17 ⋊ C2×C3×C5⋊D5
SylowC52 ⋊ C2×C17×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C2×C17×C5⋊D5
SylowC7 ⋊ C2×C3×C17×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC2×C17C5⋊(C5⋊AGL(1,𝔽7))
commutator, cosocle, hypocenterC52×C7C22×C3×C17
FrattiniC1G
Fitting, socleC2×C52×C7×C17C2×C3
LCSG ▷ C52×C7
UCSC1 ◁ C2×C17

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5950

Conjugacy classes & character table

2278 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 332);