Finite Group Databasebeta

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C2×C7×C23×AGL(1,𝔽11) #47978426

order35420
automorphism?
homologyAbelianization (H1) = C22×C5×C7×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C23×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C2×C5×C7×C23)
unambiguous semidirect product(C2×D11)⋊(C5×C7×C23)
unambiguous semidirect product(C11⋊C5)⋊(C22×C7×C23)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×C7×C23)
unambiguous semidirect product(C2×C7×D11)⋊(C5×C23)
unambiguous semidirect product(C2×D11×C23)⋊(C5×C7)
unambiguous semidirect product(C2×C7×D11×C23)⋊C5

Splittings

Fitting, socleC2×C7×C11×C23 ⋊ C2×C5
derived, SylowC11 ⋊ C22×C5×C7×C23
HallC7×C23×C11⋊C5 ⋊ C22
HallC2×C7×D11×C23 ⋊ C5
HallC7×C11×C23 ⋊ C22×C5
HallC23×C11⋊C5 ⋊ C22×C7
HallC2×D11×C23 ⋊ C5×C7
HallC7×C11⋊C5 ⋊ C22×C23
HallC2×C7×D11 ⋊ C5×C23
HallC11×C23 ⋊ C22×C5×C7
HallC7×C11 ⋊ C22×C5×C23
HallC11⋊C5 ⋊ C22×C7×C23
HallC2×D11 ⋊ C5×C7×C23

Subgroups

subgroupG/H
center, hypercenterC2×C7×C23AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C22×C5×C7×C23
FrattiniC1G
Fitting, socleC2×C7×C11×C23C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C7×C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3542

Conjugacy classes & character table

3542 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 60);