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C3×C107×AGL(1,𝔽11) #47977232

order35310
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C107 · Schur multiplier (H2) = C1

Aliases

direct productC3×C107×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C5×C107)
unambiguous semidirect product(C11⋊C5)⋊(C2×C3×C107)
unambiguous semidirect product(C3×D11)⋊(C5×C107)
unambiguous semidirect product(D11×C107)⋊(C3×C5)
unambiguous semidirect product(C3×D11×C107)⋊C5

Splittings

Fitting, socle, HallC3×C11×C107 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C3×C5×C107
HallC3×C11⋊C5×C107 ⋊ C2
HallC3×D11×C107 ⋊ C5
HallC11⋊C5×C107 ⋊ C2×C3
HallD11×C107 ⋊ C3×C5
HallC11×C107 ⋊ C2×C3×C5
HallC3×C11⋊C5 ⋊ C2×C107
HallC3×D11 ⋊ C5×C107
HallC11⋊C5 ⋊ C2×C3×C107
HallC3×C11 ⋊ C2×C5×C107
HallD11 ⋊ C3×C5×C107

Subgroups

subgroupG/H
center, hypercenterC3×C107AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C3×C5×C107
FrattiniC1G
Fitting, socleC3×C11×C107C2×C5
LCSG ▷ C11
UCSC1 ◁ C3×C107

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3531

Conjugacy classes & character table

3531 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35310, 19);