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C5×C19⋊C3×ΓL(1,𝔽8)⋊C4 #37561064

order23940
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×C19⋊C3×ΓL(1,𝔽8)⋊C4
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C5×C19⋊C3)
unambiguous semidirect product(Dic7×C19⋊C3)⋊(C3×C5)
unambiguous semidirect product(C19×ΓL(1,𝔽8)⋊C4)⋊(C3×C5)
unambiguous semidirect product#13097586⋊(C3×C5)
unambiguous semidirect product#13097587⋊(C3×C5)
unambiguous semidirect product(C5×Dic7×C19⋊C3)⋊C3
unambiguous semidirect product(C5×C19×ΓL(1,𝔽8)⋊C4)⋊C3
unambiguous semidirect product(C5×#13097586)⋊C3
unambiguous semidirect product(C5×#13097587)⋊C3

Splittings

derived, HallC7×C19 ⋊ C32×C4×C5
HallC5×ΓL(1,𝔽8)×C19⋊C3 ⋊ C4
HallC5×C19×Dic7 ⋊ C32
HallΓL(1,𝔽8)×C19⋊C3 ⋊ C4×C5
HallC5×C7×C19 ⋊ C32×C4
HallC19×Dic7 ⋊ C32×C5
HallC5×Dic7 ⋊ C3×C19⋊C3
HallC5×C19 ⋊ C3×ΓL(1,𝔽8)⋊C4
HallC5×C7 ⋊ C3×C4×C19⋊C3
HallDic7 ⋊ C3×C5×C19⋊C3
SylowC19 ⋊ C3×C5×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C4×C5×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5AGL(1,𝔽7)×C19⋊C3
commutator, hypocenterC7×C19C32×C4×C5
FrattiniC2C5×AGL(1,𝔽7)×C19⋊C3
Fitting, socleC2×C5×C7×C19C2×C32
prime radicalC2×C5×ΓL(1,𝔽8)×C19⋊C3C2
cosocleC2×C7×C19C2×C32×C5
LCSG ▷ C7×C19
UCSC1 ◁ C2×C5

144 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 2660

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 196);