Finite Group Databasebeta

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C3×#15691697 #23748619

order9477
automorphism?
homologyAbelianization (H1) = C35 · Schur multiplier (H2) = C39

Aliases

direct productC3×#15691697

Splittings

FittingC32×C13×3−1+2 ⋊ C3
SylowC13 ⋊ C3×3−1+4

Subgroups

subgroupG/H
centerC32C33×C13⋊C3
commutator, cosocleC3×C13C35
FrattiniC3C34×C13⋊C3
FittingC32×C13×3−1+2C3
socleC32×C13C34
prime radicalC32×C32⋊(C13⋊C3)C3
hypercenterC32×3−1+2C13⋊C3
hypocenterC13C3×3−1+4
LCSG ▷ C3×C13 ▷ C13
UCSC1 ◁ C32 ◁ C32×3−1+2

5588 conjugacy classes of subgroups; only the 2884 normal subgroups are shown.

normal subgroups only

This group has 5588 conjugacy classes of subgroups — too many to draw. Only its 2884 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

645 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9477, 4028);