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C17×C5⋊(D49⋊C3) #38735933

order24990
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×C5⋊(D49⋊C3)
unambiguous semidirect productC5⋊(C17×D49⋊C3)
unambiguous semidirect product(C49⋊C3)⋊(D5×C17)
unambiguous semidirect productD245⋊(C3×C17)
unambiguous semidirect product(C17×D245)⋊C3

Splittings

Fitting, HallC5×C17×C49 ⋊ C2×C3
derived, HallC5×C49 ⋊ C2×C3×C17
HallC5×C17×C49⋊C3 ⋊ C2
HallC17×D245 ⋊ C3
HallC17×C49⋊C3 ⋊ D5
HallC17×C49 ⋊ C3×D5
HallC5×C49⋊C3 ⋊ C2×C17
HallD245 ⋊ C3×C17
HallC49⋊C3 ⋊ D5×C17
HallC5×C17 ⋊ D49⋊C3
SylowC49 ⋊ C3×D5×C17
SylowC5 ⋊ C17×D49⋊C3

Subgroups

subgroupG/H
center, hypercenterC17C5⋊(D49⋊C3)
commutator, cosocle, hypocenterC5×C49C2×C3×C17
FrattiniC7C17×C5⋊AGL(1,𝔽7)
FittingC5×C17×C49C2×C3
socleC5×C7×C17AGL(1,𝔽7)
LCSG ▷ C5×C49
UCSC1 ◁ C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4165

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 23);