Finite Group Databasebeta

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C5×C7×C17×D9 #24924195

order10710
isoclinismisoclinic class of D9
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C17×D9
unambiguous semidirect productC9⋊(C2×C5×C7×C17)

Splittings

Fitting, HallC5×C7×C9×C17 ⋊ C2
derived, SylowC9 ⋊ C2×C5×C7×C17
HallC7×C9×C17 ⋊ C2×C5
HallC5×C9×C17 ⋊ C2×C7
HallC5×C7×C9 ⋊ C2×C17
HallC9×C17 ⋊ C2×C5×C7
HallC7×C9 ⋊ C2×C5×C17
HallC5×C9 ⋊ C2×C7×C17

Subgroups

subgroupG/H
center, hypercenterC5×C7×C17D9
commutator, cosocle, hypocenterC9C2×C5×C7×C17
FrattiniC3C5×D3×C7×C17
FittingC5×C7×C9×C17C2
socleC3×C5×C7×C17D3
LCSG ▷ C9
UCSC1 ◁ C5×C7×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3570 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×D9×D17, C5×D7×C17×D9, C5×D9×D119, …
maximal normal subgroup ofC5×C7×D9×D17, C5×D7×C17×D9, C5×D9×D119, …
maximal quotient ofC5×C7×C17×Dic9, C2×C5×C7×C17×D9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 10);