Finite Group Databasebeta

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C2×C107×AGL(1,𝔽11) #37555326

order23540
automorphism?
homologyAbelianization (H1) = C22×C5×C107 · Schur multiplier (H2) = C2

Aliases

direct productC2×C107×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C2×C5×C107)
unambiguous semidirect product(C2×D11)⋊(C5×C107)
unambiguous semidirect product(C11⋊C5)⋊(C22×C107)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×C107)
unambiguous semidirect product(C2×D11×C107)⋊C5

Splittings

Fitting, socleC2×C11×C107 ⋊ C2×C5
derived, SylowC11 ⋊ C22×C5×C107
HallC11⋊C5×C107 ⋊ C22
HallC2×D11×C107 ⋊ C5
HallC11×C107 ⋊ C22×C5
HallC11⋊C5 ⋊ C22×C107
HallC2×D11 ⋊ C5×C107

Subgroups

subgroupG/H
center, hypercenterC2×C107AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C22×C5×C107
FrattiniC1G
Fitting, socleC2×C11×C107C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C107

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2354

Conjugacy classes & character table

2354 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23540, 15);