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C25×D17×AGL(1,𝔽7) #49087553

order35700
automorphism?
homologyAbelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC25×D17×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C25×D17)
unambiguous semidirect product(D7×D17)⋊(C3×C25)
unambiguous semidirect product(ΓL(1,𝔽8)×D17)⋊(C2×C25)
unambiguous semidirect product(C17×AGL(1,𝔽7))⋊(C2×C25)
unambiguous semidirect product(C17⋊AGL(1,𝔽7))⋊(C2×C25)
unambiguous semidirect product(D7×C25×D17)⋊C3

Splittings

Fitting, HallC7×C17×C25 ⋊ C22×C3
derived, HallC7×C17 ⋊ C22×C3×C25
HallD7×C25×D17 ⋊ C3
HallC17×ΓL(1,𝔽8)×C25 ⋊ C22
HallΓL(1,𝔽8)×C25 ⋊ C2×D17
HallD7×D17 ⋊ C3×C25
HallC17×C25 ⋊ C2×AGL(1,𝔽7)
HallC17×ΓL(1,𝔽8) ⋊ C22×C25
HallC7×C25 ⋊ C2×C3×D17
HallΓL(1,𝔽8) ⋊ C2×C25×D17
SylowC17 ⋊ C2×C25×AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×C25×D17

Subgroups

subgroupG/H
center, hypercenterC25D17×AGL(1,𝔽7)
commutator, hypocenterC7×C17C22×C3×C25
FrattiniC5C5×D17×AGL(1,𝔽7)
FittingC7×C17×C25C22×C3
socle, cosocleC5×C7×C17C22×C3×C5
prime radicalC5×D17×AGL(1,𝔽7)C5
LCSG ▷ C7×C17
UCSC1 ◁ C25

120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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) = 2975

Conjugacy classes & character table

1750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 27);