Finite Group Databasebeta

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C3×3−1+2×#66524 #41007508

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

Aliases

direct productC3×3−1+2×#66524

Splittings

SylowC37 ⋊ C3×C9×3−1+2

Subgroups

subgroupG/H
centerC33C32×C37⋊C3
commutatorC3×C37C33×C9
FrattiniC32C33×C37⋊C3
FittingC32×3−1+2×C37C3
socleC33×C37C33
prime radicalC34×C37C32
cosocleC32×C37C34
hypercenterC32×3−1+2C37⋊C3
hypocenterC37C3×C9×3−1+2
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C33 ◁ C32×3−1+2

1148 conjugacy classes of subgroups; only the 670 normal subgroups are shown.

normal subgroups only

This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 670 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) = 8991

Conjugacy classes & character table

1485 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 3279);