Finite Group Databasebeta

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C5×C7×C9×D17 #24924188

order10710
isoclinismisoclinic class of D17
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C9×D17
unambiguous semidirect productC17⋊(C2×C5×C7×C9)

Splittings

Fitting, HallC5×C7×C9×C17 ⋊ C2
derived, SylowC17 ⋊ C2×C5×C7×C9
HallC7×C9×C17 ⋊ C2×C5
HallC5×C9×C17 ⋊ C2×C7
HallC5×C7×C17 ⋊ C2×C9
HallC9×C17 ⋊ C2×C5×C7
HallC7×C17 ⋊ C2×C5×C9
HallC5×C17 ⋊ C2×C7×C9

Subgroups

subgroupG/H
center, hypercenterC5×C7×C9D17
commutator, hypocenterC17C2×C5×C7×C9
FrattiniC3C3×C5×C7×D17
FittingC5×C7×C9×C17C2
socleC3×C5×C7×C17C2×C3
prime radicalC3×C5×C7×D17C3
cosocleC3×C17C2×C3×C5×C7
LCSG ▷ C17
UCSC1 ◁ C5×C7×C9

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3150 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×C9×#595, C5×C9×C7⋊#595, C5×C9×D7×D17, …
maximal normal subgroup ofC5×C7×C9×#595, C5×C9×C7⋊#595, C5×C9×D7×D17, …
maximal quotient ofC5×C7×C9×Dic17, C2×C5×C7×C9×D17

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 3);