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C7⋊((C23⋊C11)⋊AGL(1,𝔽5)) #47978403

order35420
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC7⋊((C23⋊C11)⋊AGL(1,𝔽5))
unambiguous semidirect product(C23⋊C11)⋊(C7⋊AGL(1,𝔽5))
unambiguous semidirect product(C7⋊(C23⋊AGL(1,𝔽5)))⋊C11

Splittings

Fitting, socle, derived, HallC5×C7×C23 ⋊ C4×C11
HallC5×C7×C23⋊C11 ⋊ C4
HallC7⋊(C23⋊AGL(1,𝔽5)) ⋊ C11
HallC7×C23⋊C11 ⋊ AGL(1,𝔽5)
HallC5×C23⋊C11 ⋊ Dic7
HallC23⋊C11 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C23 ⋊ C11×AGL(1,𝔽5)
HallC5×C23 ⋊ C11×Dic7
HallC5×C7 ⋊ Dic23⋊C11
SylowC23 ⋊ C11×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ (C23⋊C11)⋊AGL(1,𝔽5)
SylowC5 ⋊ C7⋊(Dic23⋊C11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C23C4×C11
prime radicalC7×D5×C23⋊C11C2
cosocleC7×D5×C23C2×C11
LCSG ▷ C5×C7×C23
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 805

Polycyclic presentation:

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

Conjugacy classes & character table

215 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 37);