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D35⋊AGL(1,𝔽23) #47978409

order35420
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productD35⋊AGL(1,𝔽23)
unambiguous semidirect product(C5⋊AGL(1,𝔽23))⋊D7
unambiguous semidirect product(D35⋊D23)⋊C11
unambiguous semidirect product(C7⋊AGL(1,𝔽23))⋊D5

Splittings

Fitting, socle, derived, HallC5×C7×C23 ⋊ C22×C11
HallC5×C7×C23⋊C11 ⋊ C22
HallD35⋊D23 ⋊ C11
HallC7×C23⋊C11 ⋊ C2×D5
HallC5×C23⋊C11 ⋊ C2×D7
HallC23⋊C11 ⋊ D5×D7
HallC7×C23 ⋊ C2×D5×C11
HallC5×C23 ⋊ C2×C11×D7
HallC5×C7 ⋊ C2×AGL(1,𝔽23)
SylowC23 ⋊ D5×C11×D7
SylowC7 ⋊ D5×AGL(1,𝔽23)
SylowC5 ⋊ D7×AGL(1,𝔽23)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C23C22×C11
LCSG ▷ C5×C7×C23
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 805

Polycyclic presentation:

2^2,11,5,7,23|e^a=e^6,f^a=f^22,d^b=d^4,e^b=e^6,f^c=f^2

Conjugacy classes & character table

239 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 43);