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C5×C7×C22⋊(C19⋊C3) #22547743

order7980
isoclinismisoclinic class of C22⋊(C19⋊C3)
automorphism?
homologyAbelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC5×C7×C22⋊(C19⋊C3)
unambiguous semidirect productC22⋊(C5×C7×C19⋊C3)
unambiguous semidirect productC19⋊(C5×C7×A4)
unambiguous semidirect product(C22×C5)⋊(C7×C19⋊C3)
unambiguous semidirect product(C5×C19)⋊(C7×A4)

Splittings

Fitting, socle, HallC22×C5×C7×C19 ⋊ C3
derived, HallC22×C19 ⋊ C3×C5×C7
HallC5×C7×C19 ⋊ A4
HallC22×C7×C19 ⋊ C3×C5
HallC22×C5×C19 ⋊ C3×C7
HallC22×C5×C7 ⋊ C19⋊C3
HallC7×C19 ⋊ C5×A4
HallC5×C19 ⋊ C7×A4
HallC22×C7 ⋊ C5×C19⋊C3
HallC22×C5 ⋊ C7×C19⋊C3
SylowC19 ⋊ C5×C7×A4
SylowC22 ⋊ C5×C7×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C7C22⋊(C19⋊C3)
commutator, hypocenterC22×C19C3×C5×C7
FrattiniC1G
Fitting, socleC22×C5×C7×C19C3
LCSG ▷ C22×C19
UCSC1 ◁ C5×C7

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

980 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C7×A4×C19⋊C3, C5×ΓL(1,𝔽8)×C22⋊(C19⋊C3), C5×#87704⋊A4, …
maximal normal subgroup ofC5×C7×A4×C19⋊C3, C5×ΓL(1,𝔽8)×C22⋊(C19⋊C3), C5×#87704⋊A4, …
maximal quotient ofC5×C7×C22⋊#4294, C3×C5×C7×C22⋊(C19⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 168);