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C3×C3⋊(C19⋊(Dic11⋊C5)) #49178454

order37620
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊(C19⋊(Dic11⋊C5))
unambiguous semidirect productC3⋊(C3×C19⋊(Dic11⋊C5))
unambiguous semidirect product(C11⋊C5)⋊(C3×Dic57)
unambiguous semidirect product(C3×Dic627)⋊C5

Splittings

derivedC3×C11×C19 ⋊ C3×C4×C5
HallC32×C19×C11⋊C5 ⋊ C4
HallC3×Dic627 ⋊ C5
HallC32×C11×C19 ⋊ C4×C5
HallC19×C11⋊C5 ⋊ C3×Dic3
HallC32×C11⋊C5 ⋊ Dic19
HallC11×C19 ⋊ C3×C5×Dic3
HallC32×C19 ⋊ Dic11⋊C5
HallC32×C11 ⋊ C5×Dic19
HallC11⋊C5 ⋊ C3×Dic57
SylowC19 ⋊ C3×C3⋊(Dic11⋊C5)
SylowC11 ⋊ C3×C5×Dic57
SylowC32 ⋊ C19⋊(Dic11⋊C5)

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(C19⋊AGL(1,𝔽11))
commutator, hypocenterC3×C11×C19C3×C4×C5
FrattiniC2C3×C3⋊(C19⋊AGL(1,𝔽11))
Fitting, socleC2×C32×C11×C19C2×C5
prime radicalC2×C32×C19×C11⋊C5C2
cosocleC2×C3×C11×C19C2×C3×C5
LCSG ▷ C3×C11×C19
UCSC1 ◁ C2×C3

112 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 2508

Conjugacy classes & character table

1242 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 163);