Finite Group Databasebeta

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C9×#6188 #14516723

order1944
isoclinismisoclinic class of #1088
automorphism?
homologyAbelianization (H1) = C8×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×#6188

Splittings

derivedH(3,𝔽3) ⋊ C8×C9
SylowC9×H(3,𝔽3) ⋊ C8

Subgroups

subgroupG/H
center, hypercenterC2×C3×C9#157
commutator, hypocenterH(3,𝔽3)C8×C9
Frattini, socleC2×C32C3×#157
FittingC2×C9×H(3,𝔽3)C4
prime radicalC2×C3×H(3,𝔽3)C3×C4
cosocleC3×#1084C2×C3
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C2×C3×C9

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 648

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 1117);