Finite Group Databasebeta

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3−1+2×#11758601 #41006453

order26973
automorphism?
homologyAbelianization (H1) = C32×C27 · Schur multiplier (H2) = C32

Aliases

direct product3−1+2×#11758601

Splittings

SylowC37 ⋊ C27×3−1+2

Subgroups

subgroupG/H
center, FrattiniC3×C9C32×C37⋊C3
commutatorC3×C37C32×C27
FittingC9×3−1+2×C37C3
socleC32×C37C32×C9
prime radicalC33×C37C3×C9
cosocleC3×C9×C37C33
hypercenterC9×3−1+2C37⋊C3
hypocenterC37C27×3−1+2
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C3×C9 ◁ C9×3−1+2

220 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, 2224);