Finite Group Databasebeta

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C2×C3×C7×C19×AGL(1,𝔽7) #45692554

order33516
automorphism?
homologyAbelianization (H1) = C22×C32×C7×C19 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C7×C19×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C2×C32×C7×C19)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C3×C7×C19)
unambiguous semidirect product(C2×D7)⋊(C32×C7×C19)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C3×C7×C19)
unambiguous semidirect product(C2×C3×D7)⋊(C3×C7×C19)

Splittings

Fitting, socleC2×C3×C72×C19 ⋊ C2×C3
derivedC7 ⋊ C22×C32×C7×C19
HallC3×C7×C19×ΓL(1,𝔽8) ⋊ C22
HallC2×C7×D7×C19 ⋊ C32
HallC72×C19 ⋊ C22×C32
HallC3×C7×ΓL(1,𝔽8) ⋊ C22×C19
HallC2×C7×D7 ⋊ C32×C19
SylowC72 ⋊ C22×C32×C19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7×C19AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C22×C32×C7×C19
FrattiniC1G
Fitting, socleC2×C3×C72×C19C2×C3
LCSG ▷ C7
UCSC1 ◁ C2×C3×C7×C19

248 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 136 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) = 4788

Conjugacy classes & character table

5586 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 1352);