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D3×D5×ΓL(1,𝔽8)×C29 #49141494

order36540
automorphism?
homologyAbelianization (H1) = C22×C3×C29 · Schur multiplier (H2) = C2

Aliases

direct productD3×D5×ΓL(1,𝔽8)×C29
unambiguous semidirect product(C5×D3)⋊(C2×ΓL(1,𝔽8)×C29)
unambiguous semidirect product(C3×D5)⋊(C2×ΓL(1,𝔽8)×C29)
unambiguous semidirect productD15⋊(C2×ΓL(1,𝔽8)×C29)
unambiguous semidirect product(D3×C7×D5)⋊(C3×C29)
unambiguous semidirect product(D3×C7×D5×C29)⋊C3

Splittings

Fitting, socleC3×C5×C7×C29 ⋊ C22×C3
derivedC3×C5×C7 ⋊ C22×C3×C29
HallC3×C5×ΓL(1,𝔽8)×C29 ⋊ C22
HallC3×ΓL(1,𝔽8)×C29 ⋊ C2×D5
HallC5×C7×C29 ⋊ C2×C3×D3
HallC3×C5×ΓL(1,𝔽8) ⋊ C22×C29
HallC7×C29 ⋊ C3×D3×D5
HallC5×C29 ⋊ C2×D3×ΓL(1,𝔽8)
HallC3×ΓL(1,𝔽8) ⋊ C2×D5×C29
HallC5×C7 ⋊ C2×C3×D3×C29
SylowC7 ⋊ C3×D3×D5×C29
SylowC5 ⋊ C2×D3×ΓL(1,𝔽8)×C29

Subgroups

subgroupG/H
center, hypercenterC29D3×D5×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC3×C5×C7C22×C3×C29
FrattiniC1G
Fitting, socleC3×C5×C7×C29C22×C3
LCSG ▷ C3×C5×C7
UCSC1 ◁ C29

176 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 3045

Conjugacy classes & character table

1740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 336);