Finite Group Databasebeta

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C4×C3⋊(C3⋊(C3⋊D9)) #14519008

order1944
isoclinismisoclinic class of C3⋊(C3⋊(C3⋊D9))
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C36

Aliases

direct productC4×C3⋊(C3⋊(C3⋊D9))

Splittings

FittingC33×C4×C9 ⋊ C2
derived, SylowC33×C9 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC4C3⋊(C3⋊(C3⋊D9))
commutator, hypocenterC33×C9C2×C4
FrattiniC2×C3C2×C3⋊(C3⋊(C3⋊D3))
FittingC33×C4×C9C2
socleC2×C34C2×D3
prime radicalC2×C3⋊(C3⋊(C3⋊D9))C2
cosocleC2×C33×C9C22
LCSG ▷ C33×C9
UCSC1 ◁ C4

3168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 972

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3402);