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(C17⋊AGL(1,𝔽7))⋊D23 #45659267

order32844
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(C17⋊AGL(1,𝔽7))⋊D23
unambiguous semidirect productD391⋊AGL(1,𝔽7)
unambiguous semidirect product(ΓL(1,𝔽8)⋊D23)⋊D17
unambiguous semidirect product(D119⋊D23)⋊C3

Splittings

Fitting, socle, derived, HallC7×C17×C23 ⋊ C22×C3
HallD119⋊D23 ⋊ C3
HallC17×ΓL(1,𝔽8)×C23 ⋊ C22
HallΓL(1,𝔽8)×C23 ⋊ C2×D17
HallC17×C23 ⋊ C2×AGL(1,𝔽7)
HallC17×ΓL(1,𝔽8) ⋊ C2×D23
HallC7×C23 ⋊ C2×C3×D17
HallC7×C17 ⋊ C2×C3×D23
SylowC23 ⋊ D17×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ D17×D23
SylowC17 ⋊ AGL(1,𝔽7)×D23
SylowC7 ⋊ C3×D17×D23

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C17×C23C22×C3
LCSG ▷ C7×C17×C23
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2737

Polycyclic presentation:

2^2,3,7,17,23|e^a=e^16,f^a=f^22,d^b=d^6,e^b=e^16,d^c=d^4

Conjugacy classes & character table

587 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 32);