Finite Group Databasebeta

← Prev (#41007804) Next (#41007806) →

H(3,𝔽3)×#11758606 #41007805

order26973
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C36

Aliases

direct productH(3,𝔽3)×#11758606

Splittings

FittingC9×H(3,𝔽3)×C37 ⋊ C3
SylowC37 ⋊ H(3,𝔽3)×3−1+2

Subgroups

subgroupG/H
center, FrattiniC32C33×C37⋊C3
commutator, socle, cosocleC32×C37C34
FittingC9×H(3,𝔽3)×C37C3
prime radicalC3×H(3,𝔽3)×C37⋊C3C3
hypercenterC9×H(3,𝔽3)C37⋊C3
hypocenterC37H(3,𝔽3)×3−1+2
LCSG ▷ C32×C37 ▷ C37
UCSC1 ◁ C32 ◁ C9×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) = 2997

Conjugacy classes & character table

1309 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 3576);