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D5×C17×C49⋊C3 #38735931

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

Aliases

direct productD5×C17×C49⋊C3
unambiguous semidirect productC5⋊(C2×C17×C49⋊C3)
unambiguous semidirect product(D5×C49)⋊(C3×C17)
unambiguous semidirect product(D5×C17×C49)⋊C3

Splittings

Fitting, HallC5×C17×C49 ⋊ C2×C3
derived, HallC5×C49 ⋊ C2×C3×C17
HallC5×C17×C49⋊C3 ⋊ C2
HallD5×C17×C49 ⋊ C3
HallC17×C49 ⋊ C3×D5
HallC5×C49⋊C3 ⋊ C2×C17
HallD5×C49 ⋊ C3×C17
HallC5×C17 ⋊ C2×C49⋊C3
SylowC49 ⋊ C3×D5×C17
SylowC5 ⋊ C2×C17×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC17D5×C49⋊C3
commutator, cosocle, hypocenterC5×C49C2×C3×C17
FrattiniC7D5×C17×ΓL(1,𝔽8)
FittingC5×C17×C49C2×C3
socleC5×C7×C17C2×ΓL(1,𝔽8)
LCSG ▷ C5×C49
UCSC1 ◁ C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4165

Conjugacy classes & character table

1292 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 21);