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C5×D17×C49⋊C3 #38735928

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

Aliases

direct productC5×D17×C49⋊C3
unambiguous semidirect productC17⋊(C2×C5×C49⋊C3)
unambiguous semidirect product(D17×C49)⋊(C3×C5)
unambiguous semidirect product(C5×D17×C49)⋊C3

Splittings

Fitting, HallC5×C17×C49 ⋊ C2×C3
derived, HallC17×C49 ⋊ C2×C3×C5
HallC5×C17×C49⋊C3 ⋊ C2
HallC5×D17×C49 ⋊ C3
HallC17×C49⋊C3 ⋊ C2×C5
HallD17×C49 ⋊ C3×C5
HallC5×C49 ⋊ C3×D17
HallC5×C17 ⋊ C2×C49⋊C3
SylowC49 ⋊ C3×C5×D17
SylowC17 ⋊ C2×C5×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC5D17×C49⋊C3
commutator, cosocle, hypocenterC17×C49C2×C3×C5
FrattiniC7C5×ΓL(1,𝔽8)×D17
FittingC5×C17×C49C2×C3
socleC5×C7×C17C2×ΓL(1,𝔽8)
LCSG ▷ C17×C49
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4165

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 18);