Finite Group Databasebeta

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C5×D7×AGL(1,𝔽23) #47978400

order35420
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC5×D7×AGL(1,𝔽23)
unambiguous semidirect productD23⋊(C5×C11×D7)
unambiguous semidirect product(D7×D23)⋊(C5×C11)
unambiguous semidirect product(C5×D7×D23)⋊C11
unambiguous semidirect product(C7×AGL(1,𝔽23))⋊(C2×C5)
unambiguous semidirect product(D7×C23⋊C11)⋊(C2×C5)
unambiguous semidirect product(C7⋊AGL(1,𝔽23))⋊(C2×C5)

Splittings

Fitting, socle, HallC5×C7×C23 ⋊ C22×C11
derived, HallC7×C23 ⋊ C22×C5×C11
HallC5×C7×C23⋊C11 ⋊ C22
HallC5×D7×D23 ⋊ C11
HallC7×C23⋊C11 ⋊ C22×C5
HallC5×C23⋊C11 ⋊ C2×D7
HallD7×D23 ⋊ C5×C11
HallC23⋊C11 ⋊ C2×C5×D7
HallC5×C23 ⋊ C2×C11×D7
HallC5×C7 ⋊ C2×AGL(1,𝔽23)
SylowC23 ⋊ C2×C5×C11×D7
SylowC7 ⋊ C2×C5×AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC5D7×AGL(1,𝔽23)
commutator, cosocle, hypocenterC7×C23C22×C5×C11
FrattiniC1G
Fitting, socleC5×C7×C23C22×C11
LCSG ▷ C7×C23
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 805

Conjugacy classes & character table

575 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 34);