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C3⋊(C17⋊AGL(1,𝔽23)) #38788752

order25806
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C17⋊AGL(1,𝔽23))
unambiguous semidirect productC17⋊(C3⋊AGL(1,𝔽23))
unambiguous semidirect product(C23⋊C11)⋊D51
unambiguous semidirect productD1173⋊C11

Splittings

Fitting, socle, derived, HallC3×C17×C23 ⋊ C2×C11
HallC3×C17×C23⋊C11 ⋊ C2
HallC17×C23⋊C11 ⋊ D3
HallD1173 ⋊ C11
HallC3×C23⋊C11 ⋊ D17
HallC17×C23 ⋊ D3×C11
HallC23⋊C11 ⋊ D51
HallC3×C23 ⋊ C11×D17
HallC3×C17 ⋊ AGL(1,𝔽23)
SylowC23 ⋊ C11×D51
SylowC17 ⋊ C3⋊AGL(1,𝔽23)
SylowC3 ⋊ C17⋊AGL(1,𝔽23)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C17×C23C2×C11
LCSG ▷ C3×C17×C23
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1173

Polycyclic presentation:

2,3,11,17,23|b^a=b^2,d^a=d^16,e^a=e^22,e^c=e^2

Conjugacy classes & character table

348 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25806, 24);