Finite Group Databasebeta

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C3×#595×C169 #46828143

order34476
automorphism?
homologyAbelianization (H1) = C3×C4×C169 · Schur multiplier (H2) = C1

Aliases

direct productC3×#595×C169

Splittings

Fitting, HallC3×C17×C169 ⋊ C4
derived, SylowC17 ⋊ C3×C4×C169
HallC17×C169 ⋊ C3×C4
HallC3×C17 ⋊ C4×C169

Subgroups

subgroupG/H
center, hypercenterC3×C169#595
commutator, hypocenterC17C3×C4×C169
FrattiniC13C3×C13×#595
FittingC3×C17×C169C4
socleC3×C13×C17C4×C13
prime radicalC3×C13×D17C2×C13
cosocleC13×D17C2×C3×C13
LCSG ▷ C17
UCSC1 ◁ C3×C169

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8619

Conjugacy classes & character table

4056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34476, 24);