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3−1+2×C229⋊C3 #32915352

order18549
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C32

Aliases

direct product3−1+2×C229⋊C3

Splittings

Fitting3−1+2×C229 ⋊ C3
SylowC229 ⋊ C3×3−1+2

Subgroups

subgroupG/H
center, FrattiniC3C32×C229⋊C3
commutator, socle, cosocleC3×C229C33
Fitting3−1+2×C229C3
prime radicalC32×C229⋊C3C3
hypercenter3−1+2C229⋊C3
hypocenterC229C3×3−1+2
LCSG ▷ C3×C229 ▷ C229
UCSC1 ◁ C3 ◁ 3−1+2

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2061

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18549, 42);