Finite Group Databasebeta

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C2×C9×D5×C169 #44477458

order30420
automorphism?
homologyAbelianization (H1) = C22×C9×C169 · Schur multiplier (H2) = C2

Aliases

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

Splittings

FittingC2×C5×C9×C169 ⋊ C2
derived, SylowC5 ⋊ C22×C9×C169
HallC5×C9×C169 ⋊ C22
HallC5×C169 ⋊ C22×C9
HallC5×C9 ⋊ C22×C169

Subgroups

subgroupG/H
center, hypercenterC2×C9×C169D5
commutator, hypocenterC5C22×C9×C169
FrattiniC3×C13C2×C3×D5×C13
FittingC2×C5×C9×C169C2
socleC2×C3×C5×C13C2×C3×C13
prime radicalC2×C3×D5×C13C3×C13
cosocleC3×C5×C13C22×C3×C13
LCSG ▷ C5
UCSC1 ◁ C2×C9×C169

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15210

Conjugacy classes & character table

12168 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 47);