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C2×C19×ΓL(1,𝔽8)×AGL(1,𝔽7) #45692128

order33516
automorphism?
homologyAbelianization (H1) = C22×C32×C19 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C19×ΓL(1,𝔽8)×AGL(1,𝔽7)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C19×ΓL(1,𝔽8))
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C19×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C7×AGL(1,𝔽7))⋊(C3×C19)
unambiguous semidirect product(C2×D7×ΓL(1,𝔽8))⋊(C3×C19)
unambiguous semidirect product(C2×#64423)⋊(C3×C19)
unambiguous semidirect product(C2×#64422)⋊(C3×C19)

Splittings

Fitting, socleC2×C72×C19 ⋊ C2×C32
derived, SylowC72 ⋊ C22×C32×C19
HallC19×ΓL(1,𝔽8)2 ⋊ C22
HallC2×C7×D7×C19 ⋊ C32
HallC72×C19 ⋊ C22×C32
HallΓL(1,𝔽8)2 ⋊ C22×C19
HallC2×C7×D7 ⋊ C32×C19

Subgroups

subgroupG/H
center, hypercenterC2×C19ΓL(1,𝔽8)×AGL(1,𝔽7)
commutator, cosocle, hypocenterC72C22×C32×C19
FrattiniC1G
Fitting, socleC2×C72×C19C2×C32
LCSG ▷ C72
UCSC1 ◁ C2×C19

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

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 926);