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C7×C19⋊C3×ΓL(1,𝔽16) #37561319

order23940
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C19⋊C3×ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(C7×AGL(1,𝔽5)×C19⋊C3)
unambiguous semidirect product(C19×ΓL(1,𝔽16))⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C19 ⋊ C3×C4
derivedC3×C5×C19 ⋊ C3×C4×C7
HallC3×C5×C7×C19⋊C3 ⋊ C4
HallC3×C7×C19⋊C3 ⋊ AGL(1,𝔽5)
HallC3×C5×C19⋊C3 ⋊ C4×C7
HallC5×C7×C19 ⋊ C3×Dic3
HallC3×C19⋊C3 ⋊ C7×AGL(1,𝔽5)
HallC7×C19 ⋊ C3×ΓL(1,𝔽16)
HallC5×C19 ⋊ C3×C7×Dic3
HallC5×C7 ⋊ Dic3×C19⋊C3
SylowC19 ⋊ C3×C7×ΓL(1,𝔽16)
SylowC5 ⋊ C7×Dic3×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC7C19⋊C3×ΓL(1,𝔽16)
commutator, hypocenterC3×C5×C19C3×C4×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C19C3×C4
prime radicalC3×C7×D5×C19⋊C3C2
cosocleC3×D5×C19C2×C3×C7
LCSG ▷ C3×C5×C19
UCSC1 ◁ C7

112 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 42 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) = 1995

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 451);