Finite Group Databasebeta

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C22×C5×C169⋊C9 #44477454

order30420
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×C169⋊C9

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC22×C3×C5C169⋊C3
commutator, hypocenterC169C22×C5×C9
FrattiniC3×C13C22×C5×C13⋊C3
FittingC22×C3×C5×C169C3
socle, prime radicalC22×C3×C5×C13C13⋊C3
cosocleC3×C169C22×C3×C5
LCSG ▷ C169
UCSC1 ◁ C22×C3×C5

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30420

Conjugacy classes & character table

3540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 43);