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C52×C22⋊(C19⋊C3) #19152894

order5700
isoclinismisoclinic class of C22⋊(C19⋊C3)
automorphism?
homologyAbelianization (H1) = C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC52×C22⋊(C19⋊C3)
unambiguous semidirect productC22⋊(C52×C19⋊C3)
unambiguous semidirect productC19⋊(C52×A4)
unambiguous semidirect product(C22×C5)⋊(C5×C19⋊C3)
unambiguous semidirect product(C5×C19)⋊(C5×A4)

Splittings

Fitting, socle, HallC22×C52×C19 ⋊ C3
derived, HallC22×C19 ⋊ C3×C52
HallC52×C19 ⋊ A4
HallC22×C52 ⋊ C19⋊C3
SylowC19 ⋊ C52×A4
SylowC22 ⋊ C52×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC52C22⋊(C19⋊C3)
commutator, hypocenterC22×C19C3×C52
FrattiniC1G
Fitting, socleC22×C52×C19C3
LCSG ▷ C22×C19
UCSC1 ◁ C52

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

700 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC52×A4×C19⋊C3, C52⋊C3×C22⋊(C19⋊C3), (C22⋊(C19⋊C3))⋊(C52⋊C3), …
maximal normal subgroup ofC52×A4×C19⋊C3, C52⋊C3×C22⋊(C19⋊C3), (C22⋊(C19⋊C3))⋊(C52⋊C3), …
maximal quotient ofC52×C22⋊#4294, C3×C52×C22⋊(C19⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 151);