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C5⋊(C7⋊AGL(1,𝔽23)) #31799331

order17710
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC5⋊(C7⋊AGL(1,𝔽23))
unambiguous semidirect productC7⋊(C5⋊AGL(1,𝔽23))
unambiguous semidirect product(C23⋊C11)⋊D35
unambiguous semidirect productD805⋊C11

Splittings

Fitting, socle, derived, HallC5×C7×C23 ⋊ C2×C11
HallC5×C7×C23⋊C11 ⋊ C2
HallC7×C23⋊C11 ⋊ D5
HallD805 ⋊ C11
HallC5×C23⋊C11 ⋊ D7
HallC23⋊C11 ⋊ D35
HallC7×C23 ⋊ D5×C11
HallC5×C23 ⋊ C11×D7
HallC5×C7 ⋊ AGL(1,𝔽23)
SylowC23 ⋊ C11×D35
SylowC7 ⋊ C5⋊AGL(1,𝔽23)
SylowC5 ⋊ C7⋊AGL(1,𝔽23)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C23C2×C11
LCSG ▷ C5×C7×C23
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 805

Polycyclic presentation:

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

Conjugacy classes & character table

244 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD35×AGL(1,𝔽23), D7×C5⋊AGL(1,𝔽23), D5×C7⋊AGL(1,𝔽23), …
maximal normal subgroup ofD35×AGL(1,𝔽23), D7×C5⋊AGL(1,𝔽23), D5×C7⋊AGL(1,𝔽23), …
maximal quotient ofC7⋊((C23⋊C11)⋊Dic5), C2×C5⋊(C7⋊AGL(1,𝔽23))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17710, 25);