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C3×C7×D5×C19⋊C3 #26046166

order11970
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×D5×C19⋊C3
unambiguous semidirect productC5⋊(C2×C3×C7×C19⋊C3)
unambiguous semidirect product(D5×C19)⋊(C32×C7)
unambiguous semidirect product(C3×D5×C19)⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C19 ⋊ C2×C3
derived, HallC5×C19 ⋊ C2×C32×C7
HallC3×C5×C7×C19⋊C3 ⋊ C2
HallC7×D5×C19 ⋊ C32
HallC3×C5×C19⋊C3 ⋊ C2×C7
HallC5×C7×C19 ⋊ C2×C32
HallD5×C19 ⋊ C32×C7
HallC7×C19 ⋊ C32×D5
HallC5×C7 ⋊ C2×C3×C19⋊C3
SylowC19 ⋊ C32×C7×D5
SylowC5 ⋊ C2×C3×C7×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C7D5×C19⋊C3
commutator, cosocle, hypocenterC5×C19C2×C32×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C19C2×C3
LCSG ▷ C5×C19
UCSC1 ◁ C3×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

756 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C7×(C19⋊C3)⋊AGL(1,𝔽5), C3×C7×AGL(1,𝔽5)×C19⋊C3, C3×(C19⋊C3)⋊(C7⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC3×C7×(C19⋊C3)⋊AGL(1,𝔽5), C3×C7×AGL(1,𝔽5)×C19⋊C3, C3×(C19⋊C3)⋊(C7⋊AGL(1,𝔽5)), …
maximal quotient ofC3×C7×Dic5×C19⋊C3, C2×C3×C7×D5×C19⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 95);