Finite Group Databasebeta

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3−1+2×#10587018 #28354860

order13851
automorphism?
homologyAbelianization (H1) = C32×C27 · Schur multiplier (H2) = C32

Aliases

direct product3−1+2×#10587018

Splittings

SylowC19 ⋊ C27×3−1+2

Subgroups

subgroupG/H
center, FrattiniC3×C9C32×C19⋊C3
commutatorC3×C19C32×C27
FittingC9×C19×3−1+2C3
socleC32×C19C32×C9
prime radicalC33×C19C3×C9
cosocleC3×C9×C19C33
hypercenterC9×3−1+2C19⋊C3
hypocenterC19C27×3−1+2
LCSG ▷ C3×C19 ▷ C19
UCSC1 ◁ C3×C9 ◁ C9×3−1+2

220 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4617

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 2224);