Finite Group Databasebeta

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C2×C5×D17×C49 #30659403

order16660
isoclinismisoclinic class of D17
automorphism?
homologyAbelianization (H1) = C22×C5×C49 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D17×C49
unambiguous semidirect productC17⋊(C22×C5×C49)
unambiguous semidirect product(C2×C17)⋊(C2×C5×C49)

Splittings

FittingC2×C5×C17×C49 ⋊ C2
derived, SylowC17 ⋊ C22×C5×C49
HallC5×C17×C49 ⋊ C22
HallC17×C49 ⋊ C22×C5
HallC5×C17 ⋊ C22×C49

Subgroups

subgroupG/H
center, hypercenterC2×C5×C49D17
commutator, hypocenterC17C22×C5×C49
FrattiniC7C2×C5×C7×D17
FittingC2×C5×C17×C49C2
socleC2×C5×C7×C17C2×C7
prime radicalC2×C5×C7×D17C7
cosocleC7×C17C22×C5×C7
LCSG ▷ C17
UCSC1 ◁ C2×C5×C49

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8330

Conjugacy classes & character table

4900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16660, 35);