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C2×C5×C17×C5⋊AGL(1,𝔽7) #49087854

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

Aliases

direct productC2×C5×C17×C5⋊AGL(1,𝔽7)
unambiguous semidirect product(C2×C5)⋊(C5×C17×AGL(1,𝔽7))
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C5×D5×C17)
unambiguous semidirect product(C2×D35)⋊(C3×C5×C17)
unambiguous semidirect product(C2×C5×D35)⋊(C3×C17)
unambiguous semidirect product(C2×C17×D35)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C17×D35)⋊C3

Splittings

Fitting, socleC2×C52×C7×C17 ⋊ C2×C3
derivedC5×C7 ⋊ C22×C3×C5×C17
HallC2×C5×C17×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
HallC52×C7 ⋊ C22×C3×C17
HallC7×C17 ⋊ C2×C3×C5×D5
SylowC52 ⋊ C2×C17×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C2×C5×D5×C17
SylowC7 ⋊ C2×C3×C5×D5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C17C5⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7C22×C3×C5×C17
FrattiniC1G
Fitting, socleC2×C52×C7×C17C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C2×C5×C17

192 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2380

Conjugacy classes & character table

2890 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 328);