Finite Group Databasebeta

← Prev (#46831541) Next (#46831543) →

C5×C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11)) #46831542

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

Aliases

direct productC5×C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11))
unambiguous semidirect productC3⋊(C5×ΓL(1,𝔽8)⋊AGL(1,𝔽11))
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C5×C3⋊AGL(1,𝔽7))
unambiguous semidirect product(C3⋊(C11⋊AGL(1,𝔽7)))⋊C52
unambiguous semidirect product(C3⋊(C7⋊AGL(1,𝔽11)))⋊(C3×C5)
unambiguous semidirect product(C5×C3⋊(C11⋊AGL(1,𝔽7)))⋊C5
unambiguous semidirect product(C5×C3⋊(C7⋊AGL(1,𝔽11)))⋊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
HallC3⋊(C11⋊AGL(1,𝔽7)) ⋊ C52
HallC3×C11×ΓL(1,𝔽8) ⋊ C2×C52
HallC5×C11⋊C5 ⋊ C3⋊AGL(1,𝔽7)
HallC7×C11 ⋊ C3×C52×D3
HallC3×ΓL(1,𝔽8) ⋊ C5×AGL(1,𝔽11)
SylowC11 ⋊ C52×C3⋊AGL(1,𝔽7)
SylowC7 ⋊ C3×C5×C3⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11))
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 76 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 76 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 185);