Finite Group Databasebeta

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C2×C9×C5⋊D85 #29505832

order15300
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C9×C5⋊D85
unambiguous semidirect product(C2×C5)⋊(C9×D85)
unambiguous semidirect product(C2×C17)⋊(C9×C5⋊D5)

Splittings

FittingC2×C52×C9×C17 ⋊ C2
derived, HallC52×C17 ⋊ C22×C9
HallC52×C9×C17 ⋊ C22
HallC52×C9 ⋊ C2×D17
HallC9×C17 ⋊ C2×C5⋊D5
SylowC52 ⋊ C2×C9×D17
SylowC17 ⋊ C2×C9×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC2×C9C5⋊D85
commutator, hypocenterC52×C17C22×C9
FrattiniC3C2×C3×C5⋊D85
FittingC2×C52×C9×C17C2
socleC2×C3×C52×C17C2×C3
prime radicalC2×C3×C5⋊D85C3
cosocleC3×C52×C17C22×C3
LCSG ▷ C52×C17
UCSC1 ◁ C2×C9

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7650

Conjugacy classes & character table

3852 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15300, 218);