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C5×D3×ΓL(1,𝔽8)×C11⋊C5 #46831545

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

Aliases

direct productC5×D3×ΓL(1,𝔽8)×C11⋊C5
unambiguous semidirect productC3⋊(C2×C5×ΓL(1,𝔽8)×C11⋊C5)
unambiguous semidirect product(D3×C7)⋊(C3×C5×C11⋊C5)
unambiguous semidirect product(D3×C11)⋊(C52×ΓL(1,𝔽8))
unambiguous semidirect product(C5×D3×C7)⋊(C3×C11⋊C5)
unambiguous semidirect product(C5×D3×C11)⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(D3×C11×ΓL(1,𝔽8))⋊C52
unambiguous semidirect product(D3×C7×C11⋊C5)⋊(C3×C5)
unambiguous semidirect product(C5×D3×C11×ΓL(1,𝔽8))⋊C5
unambiguous semidirect product(C5×D3×C7×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
HallD3×C11×ΓL(1,𝔽8) ⋊ C52
HallC3×C11×ΓL(1,𝔽8) ⋊ C2×C52
HallC7×C11 ⋊ C3×C52×D3
HallC3×ΓL(1,𝔽8) ⋊ C2×C5×C11⋊C5
SylowC11 ⋊ C52×D3×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C5×D3×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC5D3×ΓL(1,𝔽8)×C11⋊C5
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 90 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 90 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 188);