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D19⋊C3×C5⋊AGL(1,𝔽7) #37561201

order23940
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productD19⋊C3×C5⋊AGL(1,𝔽7)
unambiguous semidirect product(C5×D19⋊C3)⋊AGL(1,𝔽7)
unambiguous semidirect product(ΓL(1,𝔽8)×D19⋊C3)⋊D5
unambiguous semidirect product(#11716321⋊D5)⋊C3
unambiguous semidirect product(#11716322⋊D5)⋊C3
unambiguous semidirect product(D19×C5⋊AGL(1,𝔽7))⋊C3
unambiguous semidirect product(D35×D19⋊C3)⋊C3

Splittings

Fitting, socle, derived, HallC5×C7×C19 ⋊ C22×C32
HallC5×ΓL(1,𝔽8)×C19⋊C3 ⋊ C22
HallD19×D35 ⋊ C32
HallΓL(1,𝔽8)×C19⋊C3 ⋊ C2×D5
HallC7×C19 ⋊ C2×C32×D5
HallC5×C19 ⋊ C2×C3×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×C3×D19⋊C3
SylowC19 ⋊ C2×C3×C5⋊AGL(1,𝔽7)
SylowC7 ⋊ C3×D5×D19⋊C3
SylowC5 ⋊ AGL(1,𝔽7)×D19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C19C22×C32
LCSG ▷ C5×C7×C19
UCSC1

240 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 58 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) = 665

Conjugacy classes & character table

153 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 333);