Finite Group Databasebeta

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C5×C22⋊(C169⋊C9) #44477456

order30420
automorphism?
homologyAbelianization (H1) = C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC5×C22⋊(C169⋊C9)
unambiguous semidirect productC22⋊(C5×C169⋊C9)
unambiguous semidirect product(C22×C5)⋊(C169⋊C9)
unambiguous semidirect productC169⋊(C5×C22⋊C9)
unambiguous semidirect product(C5×C169)⋊(C22⋊C9)

Splittings

derived, HallC22×C169 ⋊ C5×C9
HallC22×C5×C169 ⋊ C9
HallC5×C169 ⋊ C22⋊C9
SylowC169 ⋊ C5×C22⋊C9
HallC22×C5 ⋊ C169⋊C9
SylowC22 ⋊ C5×C169⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C5C22⋊(C169⋊C3)
commutator, hypocenterC22×C169C5×C9
FrattiniC3×C13C5×C22⋊(C13⋊C3)
FittingC22×C3×C5×C169C3
socle, prime radicalC22×C3×C5×C13C13⋊C3
cosocleC22×C3×C169C3×C5
LCSG ▷ C22×C169
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15210

Conjugacy classes & character table

3420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 45);