Finite Group Databasebeta

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C2×C9×C25×D17 #29505644

order15300
isoclinismisoclinic class of D17
automorphism?
homologyAbelianization (H1) = C22×C9×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×C25×D17
unambiguous semidirect productC17⋊(C22×C9×C25)
unambiguous semidirect product(C2×C17)⋊(C2×C9×C25)

Splittings

FittingC2×C9×C17×C25 ⋊ C2
derived, SylowC17 ⋊ C22×C9×C25
HallC9×C17×C25 ⋊ C22
HallC17×C25 ⋊ C22×C9
HallC9×C17 ⋊ C22×C25

Subgroups

subgroupG/H
center, hypercenterC2×C9×C25D17
commutator, hypocenterC17C22×C9×C25
FrattiniC3×C5C2×C3×C5×D17
FittingC2×C9×C17×C25C2
socleC2×C3×C5×C17C2×C3×C5
prime radicalC2×C3×C5×D17C3×C5
cosocleC3×C5×C17C22×C3×C5
LCSG ▷ C17
UCSC1 ◁ C2×C9×C25

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7650

Conjugacy classes & character table

4500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15300, 30);