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C2×C7×AGL(1,𝔽7)×C19⋊C3 #45692115

order33516
automorphism?
homologyAbelianization (H1) = C22×C32×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C7×AGL(1,𝔽7)×C19⋊C3
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C7×C19⋊C3)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C7×C19⋊C3)
unambiguous semidirect product(C2×D7×C19⋊C3)⋊(C3×C7)
unambiguous semidirect product(C2×C19×AGL(1,𝔽7))⋊(C3×C7)
unambiguous semidirect product(C2×#11716325)⋊(C3×C7)
unambiguous semidirect product(C2×#11716326)⋊(C3×C7)

Splittings

Fitting, socleC2×C72×C19 ⋊ C2×C32
derivedC7×C19 ⋊ C22×C32×C7
HallC7×ΓL(1,𝔽8)×C19⋊C3 ⋊ C22
HallC2×C7×D7×C19 ⋊ C32
HallC72×C19 ⋊ C22×C32
HallC2×C7×D7 ⋊ C3×C19⋊C3
SylowC72 ⋊ C22×C3×C19⋊C3
SylowC19 ⋊ C2×C3×C7×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, hypercenterC2×C7AGL(1,𝔽7)×C19⋊C3
commutator, cosocle, hypocenterC7×C19C22×C32×C7
FrattiniC1G
Fitting, socleC2×C72×C19C2×C32
LCSG ▷ C7×C19
UCSC1 ◁ C2×C7

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

normal subgroups only

This group has 248 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) = 1596

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 913);