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C2×C52×D49⋊C3 #28412950

order14700
isoclinismisoclinic class of D49⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C52×D49⋊C3
unambiguous semidirect productD49⋊(C2×C3×C52)
unambiguous semidirect product(C49⋊C3)⋊(C22×C52)
unambiguous semidirect product(C2×D49)⋊(C3×C52)
unambiguous semidirect product(C2×C49⋊C3)⋊(C2×C52)
unambiguous semidirect product(C2×C5×D49)⋊(C3×C5)

Splittings

FittingC2×C52×C49 ⋊ C2×C3
derived, SylowC49 ⋊ C22×C3×C52
HallC2×C52×D49 ⋊ C3
HallC52×C49⋊C3 ⋊ C22
HallC52×C49 ⋊ C22×C3
HallC2×D49 ⋊ C3×C52
HallC49⋊C3 ⋊ C22×C52

Subgroups

subgroupG/H
center, hypercenterC2×C52D49⋊C3
commutator, cosocle, hypocenterC49C22×C3×C52
FrattiniC7C2×C52×AGL(1,𝔽7)
FittingC2×C52×C49C2×C3
socleC2×C52×C7AGL(1,𝔽7)
LCSG ▷ C49
UCSC1 ◁ C2×C52

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

700 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 129);