Finite Group Databasebeta

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#14519007

order1944
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C36

Aliases

No aliases for this group.

Splittings

SylowC33×C9 ⋊ Q8

Subgroups

subgroupG/H
centerC2C2×C3⋊(C3⋊(C3⋊D9))
commutator, cosocleC2×C33×C9C22
FrattiniC2×C3C2×C3⋊(C3⋊(C3⋊D3))
FittingC33×C4×C9C2
socle, prime radicalC2×C34C2×D3
hypercenterC4C3⋊(C3⋊(C3⋊D9))
hypocenterC33×C9Q8
LCSG ▷ C2×C33×C9 ▷ C33×C9
UCSC1 ◁ C2 ◁ C4

2376 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1944

Polycyclic presentation:

2^3,3^5|a^2=c,b^2=c,g^3=h,b^a=bc,d^a=d^2,e^a=e^2,f^a=f^2,g^a=g^2h^2,h^a=h^2

Conjugacy classes & character table

489 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3401);