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C3×C3⋊(C11⋊(C19⋊AGL(1,𝔽5))) #49178677

order37620
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊(C11⋊(C19⋊AGL(1,𝔽5)))
unambiguous semidirect productC3⋊(C3×C11⋊(C19⋊AGL(1,𝔽5)))
unambiguous semidirect productC11⋊(C3×C3⋊(C19⋊AGL(1,𝔽5)))

Splittings

Fitting, socle, HallC32×C5×C11×C19 ⋊ C4
derivedC3×C5×C11×C19 ⋊ C3×C4
HallC32×C11×C19 ⋊ AGL(1,𝔽5)
HallC5×C11×C19 ⋊ C3×Dic3
HallC32×C5×C19 ⋊ Dic11
HallC32×C5×C11 ⋊ Dic19
HallC11×C19 ⋊ C3×ΓL(1,𝔽16)
HallC32×C19 ⋊ C11⋊AGL(1,𝔽5)
HallC32×C11 ⋊ C19⋊AGL(1,𝔽5)
HallC5×C19 ⋊ C3×Dic33
HallC5×C11 ⋊ C3×Dic57
HallC32×C5 ⋊ Dic209
SylowC19 ⋊ C3×C3⋊(C11⋊AGL(1,𝔽5))
SylowC11 ⋊ C3×C3⋊(C19⋊AGL(1,𝔽5))
SylowC32 ⋊ C11⋊(C19⋊AGL(1,𝔽5))
SylowC5 ⋊ C3×Dic627

Subgroups

subgroupG/H
center, hypercenterC3C3⋊(C11⋊(C19⋊AGL(1,𝔽5)))
commutator, hypocenterC3×C5×C11×C19C3×C4
FrattiniC1G
Fitting, socleC32×C5×C11×C19C4
prime radicalC32×D5×C11×C19C2
cosocleC3×D5×C11×C19C2×C3
LCSG ▷ C3×C5×C11×C19
UCSC1 ◁ C3

112 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 6270

Conjugacy classes & character table

3771 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 386);