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C5×D169⋊C9 #29503539

order15210
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×D169⋊C9
unambiguous semidirect productD169⋊(C5×C9)
unambiguous semidirect product(C169⋊C9)⋊(C2×C5)
unambiguous semidirect product(C5×D169)⋊C9

Splittings

derived, SylowC169 ⋊ C2×C5×C9
HallC5×C169⋊C9 ⋊ C2
HallC5×D169 ⋊ C9
HallC169⋊C9 ⋊ C2×C5
HallC5×C169 ⋊ C2×C9
HallD169 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C5D169⋊C3
commutator, hypocenterC169C2×C5×C9
FrattiniC3×C13C5×D13⋊C3
FittingC3×C5×C169C2×C3
socleC3×C5×C13D13⋊C3
prime radicalC3×C5×D169C3
cosocleC3×C169C2×C3×C5
LCSG ▷ C169
UCSC1 ◁ C3×C5

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7605

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×#10621721⋊C9, #16809977⋊C9, D5×D169⋊C9, …
maximal normal subgroup ofC5×#10621721⋊C9, #16809977⋊C9, D5×D169⋊C9, …
maximal quotient ofC5×Dic169⋊C9, C2×C5×D169⋊C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15210, 2);