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C5×C17⋊(D49⋊C3) #38735930

order24990
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17⋊(D49⋊C3)
unambiguous semidirect productC17⋊(C5×D49⋊C3)
unambiguous semidirect product(C49⋊C3)⋊(C5×D17)
unambiguous semidirect productD833⋊(C3×C5)
unambiguous semidirect product(C5×D833)⋊C3

Splittings

Fitting, HallC5×C17×C49 ⋊ C2×C3
derived, HallC17×C49 ⋊ C2×C3×C5
HallC5×C17×C49⋊C3 ⋊ C2
HallC5×D833 ⋊ C3
HallC17×C49⋊C3 ⋊ C2×C5
HallD833 ⋊ C3×C5
HallC5×C49⋊C3 ⋊ D17
HallC5×C49 ⋊ C3×D17
HallC49⋊C3 ⋊ C5×D17
HallC5×C17 ⋊ D49⋊C3
SylowC49 ⋊ C3×C5×D17
SylowC17 ⋊ C5×D49⋊C3

Subgroups

subgroupG/H
center, hypercenterC5C17⋊(D49⋊C3)
commutator, cosocle, hypocenterC17×C49C2×C3×C5
FrattiniC7C5×C17⋊AGL(1,𝔽7)
FittingC5×C17×C49C2×C3
socleC5×C7×C17AGL(1,𝔽7)
LCSG ▷ C17×C49
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4165

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 20);