Finite Group Databasebeta

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C2×D5×C169⋊C9 #44477433

order30420
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×C169⋊C9
unambiguous semidirect productC5⋊(C22×C169⋊C9)
unambiguous semidirect product(C2×C5)⋊(C2×C169⋊C9)
unambiguous semidirect product(C2×D5×C169)⋊C9

Splittings

derived, HallC5×C169 ⋊ C22×C9
HallC5×C169⋊C9 ⋊ C22
HallC2×D5×C169 ⋊ C9
SylowC169 ⋊ C2×C9×D5
SylowC5 ⋊ C22×C169⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×C169⋊C3
commutator, hypocenterC5×C169C22×C9
FrattiniC3×C13C2×D5×C13⋊C3
FittingC2×C3×C5×C169C2×C3
socleC2×C3×C5×C13C2×C13⋊C3
prime radicalC2×C3×D5×C13C13⋊C3
cosocleC3×C5×C169C22×C3
LCSG ▷ C5×C169
UCSC1 ◁ C2×C3

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15210

Conjugacy classes & character table

1416 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 22);