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D5×ΓL(1,𝔽8)×D13⋊C3 #30655302

order16380
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productD5×ΓL(1,𝔽8)×D13⋊C3
unambiguous semidirect product(C5×D13⋊C3)⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect product(D5×C13⋊C3)⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect product(C5⋊(D13⋊C3))⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D5×D13⋊C3)⋊C3
unambiguous semidirect product(D5×#10587716)⋊C3
unambiguous semidirect product(D5×#10587717)⋊C3
unambiguous semidirect product(D5×ΓL(1,𝔽8)×D13)⋊C3

Splittings

Fitting, socle, derived, HallC5×C7×C13 ⋊ C22×C32
HallC5×ΓL(1,𝔽8)×C13⋊C3 ⋊ C22
HallC7×D5×D13 ⋊ C32
HallΓL(1,𝔽8)×C13⋊C3 ⋊ C2×D5
HallD5×D13 ⋊ C3×ΓL(1,𝔽8)
HallC7×C13 ⋊ C2×C32×D5
HallC5×C13 ⋊ C22×C3×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×C3×D13⋊C3
SylowC13 ⋊ C2×C3×D5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×D5×D13⋊C3
SylowC5 ⋊ C2×ΓL(1,𝔽8)×D13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C13C22×C32
LCSG ▷ C5×C7×C13
UCSC1

240 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 65 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) = 455

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 352);