Finite Group Databasebeta

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C9×#15688532 #41007514

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

Aliases

direct productC9×#15688532

Splittings

FittingC9×3−1+2×C37 ⋊ C3
SylowC37 ⋊ C9×#737

Subgroups

subgroupG/H
centerC3×C9C32×C37⋊C3
commutatorC3×C37C33×C9
FrattiniC32C33×C37⋊C3
FittingC9×3−1+2×C37C3
socle, cosocleC32×C37C34
prime radicalC3×C32⋊(C37⋊C3)C32
hypercenterC9×3−1+2C37⋊C3
hypocenterC37C9×#737
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C3×C9 ◁ C9×3−1+2

986 conjugacy classes of subgroups.

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, 3285);