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C3×C5×C23×AGL(1,𝔽11) #49182115

order37950
automorphism?
homologyAbelianization (H1) = C2×C3×C52×C23 · Schur multiplier (H2) = C5

Aliases

direct productC3×C5×C23×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C52×C23)
unambiguous semidirect product(C11⋊C5)⋊(C2×C3×C5×C23)
unambiguous semidirect product(C3×D11)⋊(C52×C23)
unambiguous semidirect product(C5×D11)⋊(C3×C5×C23)
unambiguous semidirect product(C3×C5×D11)⋊(C5×C23)
unambiguous semidirect product(D11×C23)⋊(C3×C52)
unambiguous semidirect product(C3×D11×C23)⋊C52
unambiguous semidirect product(C5×D11×C23)⋊(C3×C5)
unambiguous semidirect product(C3×C5×D11×C23)⋊C5

Splittings

Fitting, socleC3×C5×C11×C23 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C3×C52×C23
HallC3×C5×C23×C11⋊C5 ⋊ C2
HallC5×C23×C11⋊C5 ⋊ C2×C3
HallC3×D11×C23 ⋊ C52
HallC3×C5×C11⋊C5 ⋊ C2×C23
HallC3×C11×C23 ⋊ C2×C52
HallD11×C23 ⋊ C3×C52
HallC5×C11⋊C5 ⋊ C2×C3×C23
HallC11×C23 ⋊ C2×C3×C52
HallC3×D11 ⋊ C52×C23
HallC3×C11 ⋊ C2×C52×C23
HallD11 ⋊ C3×C52×C23

Subgroups

subgroupG/H
center, hypercenterC3×C5×C23AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C3×C52×C23
FrattiniC1G
Fitting, socleC3×C5×C11×C23C2×C5
LCSG ▷ C11
UCSC1 ◁ C3×C5×C23

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3795

Conjugacy classes & character table

3795 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 52);