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C5×ΓL(1,𝔽8)⋊((C19⋊C3)⋊C4) #37561063

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

Aliases

direct productC5×ΓL(1,𝔽8)⋊((C19⋊C3)⋊C4)
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×(C19⋊C3)⋊C4)
unambiguous semidirect product(C19⋊C3)⋊(C5×ΓL(1,𝔽8)⋊C4)
unambiguous semidirect product((C19⋊C3)⋊Dic7)⋊(C3×C5)
unambiguous semidirect product(ΓL(1,𝔽8)⋊Dic19)⋊(C3×C5)
unambiguous semidirect product#13097588⋊(C3×C5)
unambiguous semidirect product#13097589⋊(C3×C5)
unambiguous semidirect product(C5×(C19⋊C3)⋊Dic7)⋊C3
unambiguous semidirect product(C5×ΓL(1,𝔽8)⋊Dic19)⋊C3
unambiguous semidirect product(C5×#13097588)⋊C3
unambiguous semidirect product(C5×#13097589)⋊C3

Splittings

derived, HallC7×C19 ⋊ C32×C4×C5
HallC5×ΓL(1,𝔽8)×C19⋊C3 ⋊ C4
HallC5×Dic133 ⋊ C32
HallΓL(1,𝔽8)×C19⋊C3 ⋊ C4×C5
HallC5×C7×C19 ⋊ C32×C4
HallDic133 ⋊ C32×C5
HallC5×C19 ⋊ C3×ΓL(1,𝔽8)⋊C4
HallC5×C7 ⋊ C3×(C19⋊C3)⋊C4
SylowC19 ⋊ C3×C5×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C5×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)⋊(D19⋊C3)
commutator, hypocenterC7×C19C32×C4×C5
FrattiniC2C5×ΓL(1,𝔽8)⋊(D19⋊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 56 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 56 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 195);