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C2×C5×C13⋊C3×AGL(1,𝔽7) #30655304

order16380
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C5×C13⋊C3×AGL(1,𝔽7)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C5×C13⋊C3)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C5×C13⋊C3)
unambiguous semidirect product(C2×D7×C13⋊C3)⋊(C3×C5)
unambiguous semidirect product(C2×C13×AGL(1,𝔽7))⋊(C3×C5)
unambiguous semidirect product(C2×#10587720)⋊(C3×C5)
unambiguous semidirect product(C2×#10587721)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C13×AGL(1,𝔽7))⋊C3
unambiguous semidirect product(C2×C5×#10587720)⋊C3
unambiguous semidirect product(C2×C5×#10587721)⋊C3
unambiguous semidirect product(C2×C5×D7×C13⋊C3)⋊C3

Splittings

Fitting, socleC2×C5×C7×C13 ⋊ C2×C32
derived, HallC7×C13 ⋊ C22×C32×C5
HallC5×ΓL(1,𝔽8)×C13⋊C3 ⋊ C22
HallC2×C5×C13×D7 ⋊ C32
HallΓL(1,𝔽8)×C13⋊C3 ⋊ C22×C5
HallC5×C7×C13 ⋊ C22×C32
HallC2×C13×D7 ⋊ C32×C5
HallC2×C5×D7 ⋊ C3×C13⋊C3
HallC5×C13 ⋊ C2×C3×AGL(1,𝔽7)
HallC5×C7 ⋊ C22×C3×C13⋊C3
HallC2×D7 ⋊ C3×C5×C13⋊C3
SylowC13 ⋊ C2×C3×C5×AGL(1,𝔽7)
SylowC7 ⋊ C22×C3×C5×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5C13⋊C3×AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C13C22×C32×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C13C2×C32
LCSG ▷ C7×C13
UCSC1 ◁ C2×C5

240 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 910

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 354);