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C17×C22⋊(C7⋊(C52⋊C3)) #49088034

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

Aliases

direct productC17×C22⋊(C7⋊(C52⋊C3))
unambiguous semidirect productC22⋊(C17×C7⋊(C52⋊C3))
unambiguous semidirect productC7⋊(C17×C22⋊(C52⋊C3))
unambiguous semidirect productC52⋊(C17×C22⋊ΓL(1,𝔽8))
unambiguous semidirect product(C22×C17)⋊(C7⋊(C52⋊C3))
unambiguous semidirect product(C7×C17)⋊(C22⋊(C52⋊C3))
unambiguous semidirect product(C52×C17)⋊(C22⋊ΓL(1,𝔽8))

Splittings

Fitting, socle, HallC22×C52×C7×C17 ⋊ C3
derived, HallC22×C52×C7 ⋊ C3×C17
HallC52×C7×C17 ⋊ A4
HallC22×C52×C17 ⋊ ΓL(1,𝔽8)
HallC22×C7×C17 ⋊ C52⋊C3
HallC52×C17 ⋊ C22⋊ΓL(1,𝔽8)
HallC52×C7 ⋊ A4×C17
HallC7×C17 ⋊ C22⋊(C52⋊C3)
HallC22×C52 ⋊ C17×ΓL(1,𝔽8)
HallC22×C17 ⋊ C7⋊(C52⋊C3)
HallC22×C7 ⋊ C17×C52⋊C3
SylowC52 ⋊ C17×C22⋊ΓL(1,𝔽8)
SylowC7 ⋊ C17×C22⋊(C52⋊C3)
SylowC22 ⋊ C17×C7⋊(C52⋊C3)

Subgroups

subgroupG/H
center, hypercenterC17C22⋊(C7⋊(C52⋊C3))
commutator, cosocle, hypocenterC22×C52×C7C3×C17
FrattiniC1G
Fitting, socleC22×C52×C7×C17C3
LCSG ▷ C22×C52×C7
UCSC1 ◁ C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3570

Conjugacy classes & character table

4012 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 508);