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C5×C11⋊C5×C3⋊AGL(1,𝔽7) #46831543

order34650
automorphism?
homologyAbelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C11⋊C5×C3⋊AGL(1,𝔽7)
unambiguous semidirect productC3⋊(C5×AGL(1,𝔽7)×C11⋊C5)
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×D3×C11⋊C5)
unambiguous semidirect productD21⋊(C3×C5×C11⋊C5)
unambiguous semidirect product(C5×D21)⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×C3⋊AGL(1,𝔽7))⋊C52
unambiguous semidirect product(D21×C11⋊C5)⋊(C3×C5)
unambiguous semidirect product(C5×C11×C3⋊AGL(1,𝔽7))⋊C5
unambiguous semidirect product(C5×D21×C11⋊C5)⋊C3

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C2×C3×C5
derivedC3×C7×C11 ⋊ C2×C3×C52
HallC3×C5×ΓL(1,𝔽8)×C11⋊C5 ⋊ C2
HallC5×C7×C11⋊C5 ⋊ C3×D3
HallC11×C3⋊AGL(1,𝔽7) ⋊ C52
HallC3×C11×ΓL(1,𝔽8) ⋊ C2×C52
HallC7×C11 ⋊ C3×C52×D3
HallC3×ΓL(1,𝔽8) ⋊ C2×C5×C11⋊C5
SylowC11 ⋊ C52×C3⋊AGL(1,𝔽7)
SylowC7 ⋊ C3×C5×D3×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC5C11⋊C5×C3⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC3×C7×C11C2×C3×C52
FrattiniC1G
Fitting, socleC3×C5×C7×C11C2×C3×C5
LCSG ▷ C3×C7×C11
UCSC1 ◁ C5

288 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1155

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 186);