Finite Group Databasebeta

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C5×C17×D49⋊C3 #38735929

order24990
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17×D49⋊C3
unambiguous semidirect productD49⋊(C3×C5×C17)
unambiguous semidirect product(C49⋊C3)⋊(C2×C5×C17)
unambiguous semidirect product(C5×D49)⋊(C3×C17)
unambiguous semidirect product(C17×D49)⋊(C3×C5)
unambiguous semidirect product(C5×C17×D49)⋊C3

Splittings

Fitting, HallC5×C17×C49 ⋊ C2×C3
derived, SylowC49 ⋊ C2×C3×C5×C17
HallC5×C17×C49⋊C3 ⋊ C2
HallC5×C17×D49 ⋊ C3
HallC17×C49⋊C3 ⋊ C2×C5
HallC17×D49 ⋊ C3×C5
HallC17×C49 ⋊ C2×C3×C5
HallC5×C49⋊C3 ⋊ C2×C17
HallC5×D49 ⋊ C3×C17
HallC5×C49 ⋊ C2×C3×C17
HallC49⋊C3 ⋊ C2×C5×C17
HallD49 ⋊ C3×C5×C17

Subgroups

subgroupG/H
center, hypercenterC5×C17D49⋊C3
commutator, cosocle, hypocenterC49C2×C3×C5×C17
FrattiniC7C5×C17×AGL(1,𝔽7)
FittingC5×C17×C49C2×C3
socleC5×C7×C17AGL(1,𝔽7)
LCSG ▷ C49
UCSC1 ◁ C5×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4165

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 19);