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C52×C22⋊(C49⋊C3) #28413006

order14700
automorphism?
homologyAbelianization (H1) = C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC52×C22⋊(C49⋊C3)
unambiguous semidirect productC22⋊(C52×C49⋊C3)
unambiguous semidirect product(C22×C5)⋊(C5×C49⋊C3)
unambiguous semidirect productC49⋊(C52×A4)
unambiguous semidirect product(C5×C49)⋊(C5×A4)

Splittings

Fitting, HallC22×C52×C49 ⋊ C3
derived, HallC22×C49 ⋊ C3×C52
HallC52×C49 ⋊ A4
HallC22×C52 ⋊ C49⋊C3
SylowC49 ⋊ C52×A4
SylowC22 ⋊ C52×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC52C22⋊(C49⋊C3)
commutator, cosocle, hypocenterC22×C49C3×C52
FrattiniC7C52×C22⋊ΓL(1,𝔽8)
FittingC22×C52×C49C3
socleC22×C52×C7ΓL(1,𝔽8)
LCSG ▷ C22×C49
UCSC1 ◁ C52

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 185);