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H(3,𝔽3)×#11923958 #44534952

order31347
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C36

Aliases

direct productH(3,𝔽3)×#11923958

Splittings

SylowC43 ⋊ H(3,𝔽3)×3−1+2

Subgroups

subgroupG/H
center, FrattiniC32C33×C43⋊C3
commutator, socle, cosocleC32×C43C34
Fitting, prime radicalC32×H(3,𝔽3)×C43C3
hypercenterC32×H(3,𝔽3)C43⋊C3
hypocenterC43H(3,𝔽3)×3−1+2
LCSG ▷ C32×C43 ▷ C43
UCSC1 ◁ C32 ◁ C32×H(3,𝔽3)

1244 conjugacy classes of subgroups; only the 316 normal subgroups are shown.

normal subgroups only

This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 316 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degreeμt(G) = 3483

Conjugacy classes & character table

1507 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 3575);