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C4×C5×C19⋊C3 #11765876

order1140
isoclinismisoclinic class of C19⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C19⋊C3
unambiguous semidirect product(C4×C19)⋊(C3×C5)
unambiguous semidirect product(C4×C5×C19)⋊C3

Splittings

Fitting, HallC4×C5×C19 ⋊ C3
derived, SylowC19 ⋊ C3×C4×C5
HallC5×C19 ⋊ C3×C4
HallC4×C19 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC4×C5C19⋊C3
commutator, hypocenterC19C3×C4×C5
FrattiniC2C2×C5×C19⋊C3
FittingC4×C5×C19C3
socleC2×C5×C19C2×C3
prime radicalC2×C5×C19⋊C3C2
cosocleC2×C19C2×C3×C5
LCSG ▷ C19
UCSC1 ◁ C4×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 380

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C5×#4296, C5×Dic3×C19⋊C3, C3×C4×C5×C19⋊C3, …
maximal normal subgroup ofC4×C5×#4296, C3×C4×C5×C19⋊C3, C4×C5×C11×C19⋊C3, …
maximal quotient ofC4×C5×#4294, C5×Dic3×C19⋊C3, C3×C4×C5×C19⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1140, 4);