Finite Group Databasebeta

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C2×C9×C17×C5⋊D5 #29505831

order15300
isoclinismisoclinic class of C5⋊D5
automorphism?
homologyAbelianization (H1) = C22×C9×C17 · Schur multiplier (H2) = C2×C5

Aliases

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

Splittings

FittingC2×C52×C9×C17 ⋊ C2
derived, SylowC52 ⋊ C22×C9×C17
HallC52×C9×C17 ⋊ C22
HallC52×C17 ⋊ C22×C9
HallC52×C9 ⋊ C22×C17

Subgroups

subgroupG/H
center, hypercenterC2×C9×C17C5⋊D5
commutator, hypocenterC52C22×C9×C17
FrattiniC3C2×C3×C17×C5⋊D5
FittingC2×C52×C9×C17C2
socleC2×C3×C52×C17C2×C3
prime radicalC2×C3×C17×C5⋊D5C3
cosocleC3×C52C22×C3×C17
LCSG ▷ C52
UCSC1 ◁ C2×C9×C17

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7650

Conjugacy classes & character table

4284 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15300, 217);