Finite Group Databasebeta

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C5×C7×C17×C7⋊C9 #49154153

order37485
automorphism?
homologyAbelianization (H1) = C5×C7×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C17×C7⋊C9
unambiguous semidirect productC7⋊(C5×C7×C9×C17)
unambiguous semidirect product(C5×C7)⋊(C7×C9×C17)
unambiguous semidirect product(C7×C17)⋊(C5×C7×C9)
unambiguous semidirect product(C5×C7×C17)⋊(C7×C9)

Splittings

derivedC7 ⋊ C5×C7×C9×C17
HallC5×C72×C17 ⋊ C9
HallC72×C17 ⋊ C5×C9
HallC5×C72 ⋊ C9×C17
SylowC72 ⋊ C5×C9×C17

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7×C17ΓL(1,𝔽8)
commutator, hypocenterC7C5×C7×C9×C17
FrattiniC3C5×C7×C17×ΓL(1,𝔽8)
Fitting, socle, prime radicalC3×C5×C72×C17C3
cosocleC3×C7C3×C5×C7×C17
LCSG ▷ C7
UCSC1 ◁ C3×C5×C7×C17

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5355

Conjugacy classes & character table

8925 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37485, 7);