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C17×C5⋊(D7⋊C9) #24924208

order10710
automorphism?
homologyAbelianization (H1) = C2×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×C5⋊(D7⋊C9)
unambiguous semidirect productC5⋊(C17×D7⋊C9)
unambiguous semidirect product(C7⋊C9)⋊(D5×C17)
unambiguous semidirect productD35⋊(C9×C17)
unambiguous semidirect product(C17×D35)⋊C9

Splittings

derived, HallC5×C7 ⋊ C2×C9×C17
HallC5×C17×C7⋊C9 ⋊ C2
HallC17×D35 ⋊ C9
HallC17×C7⋊C9 ⋊ D5
HallC5×C7×C17 ⋊ C2×C9
HallC5×C7⋊C9 ⋊ C2×C17
HallC7×C17 ⋊ C9×D5
HallC5×C17 ⋊ D7⋊C9
HallD35 ⋊ C9×C17
HallC7⋊C9 ⋊ D5×C17
SylowC7 ⋊ C9×D5×C17
SylowC5 ⋊ C17×D7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C17C5⋊AGL(1,𝔽7)
commutator, hypocenterC5×C7C2×C9×C17
FrattiniC3C17×C5⋊AGL(1,𝔽7)
Fitting, socleC3×C5×C7×C17C2×C3
prime radicalC3×C17×D35C3
cosocleC3×C5×C7C2×C3×C17
LCSG ▷ C5×C7
UCSC1 ◁ C3×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

867 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD17×C5⋊(D7⋊C9), D5×C17×D7⋊C9, D85⋊(D7⋊C9), …
maximal normal subgroup ofD17×C5⋊(D7⋊C9), D5×C17×D7⋊C9, D85⋊(D7⋊C9), …
maximal quotient ofC17×(C7⋊C9)⋊Dic5, C2×C17×C5⋊(D7⋊C9)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 23);