Finite Group Databasebeta

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C3×3−1+2×#66526 #41008638

order26973
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C35

Aliases

direct productC3×3−1+2×#66526
unambiguous semidirect product(C37⋊C3)⋊(C9×3−1+2)

Splittings

FittingC3×3−1+2×C37 ⋊ C9
SylowC37 ⋊ C3×C9×3−1+2

Subgroups

subgroupG/H
centerC32C32×#66526
commutatorC3×C37C33×C9
FrattiniC3C33×#66526
FittingC3×3−1+2×C37C9
socleC32×C37C32×C9
prime radicalC33×C37⋊C3C32
cosocleC3×C37⋊C3C34
hypercenterC3×3−1+2#66526
hypocenterC37C3×C9×3−1+2
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C32 ◁ C3×3−1+2

1148 conjugacy classes of subgroups; only the 468 normal subgroups are shown.

normal subgroups only

This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 468 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) = 999

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 4409);