Finite Group Databasebeta

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C2×C5×C7×AGL(1,𝔽23) #47978411

order35420
automorphism?
homologyAbelianization (H1) = C22×C5×C7×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×AGL(1,𝔽23)
unambiguous semidirect productD23⋊(C2×C5×C7×C11)
unambiguous semidirect product(C2×D23)⋊(C5×C7×C11)
unambiguous semidirect product(C23⋊C11)⋊(C22×C5×C7)
unambiguous semidirect product(C2×C5×D23)⋊(C7×C11)
unambiguous semidirect product(C2×C23⋊C11)⋊(C2×C5×C7)
unambiguous semidirect product(C2×C7×D23)⋊(C5×C11)
unambiguous semidirect product(C2×C5×C7×D23)⋊C11

Splittings

Fitting, socleC2×C5×C7×C23 ⋊ C2×C11
derived, SylowC23 ⋊ C22×C5×C7×C11
HallC5×C7×C23⋊C11 ⋊ C22
HallC2×C5×C7×D23 ⋊ C11
HallC7×C23⋊C11 ⋊ C22×C5
HallC5×C23⋊C11 ⋊ C22×C7
HallC5×C7×C23 ⋊ C22×C11
HallC2×C7×D23 ⋊ C5×C11
HallC2×C5×D23 ⋊ C7×C11
HallC23⋊C11 ⋊ C22×C5×C7
HallC7×C23 ⋊ C22×C5×C11
HallC5×C23 ⋊ C22×C7×C11
HallC2×D23 ⋊ C5×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7AGL(1,𝔽23)
commutator, cosocle, hypocenterC23C22×C5×C7×C11
FrattiniC1G
Fitting, socleC2×C5×C7×C23C2×C11
LCSG ▷ C23
UCSC1 ◁ C2×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1610

Conjugacy classes & character table

1610 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 45);