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#14517258

order1944
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C34

Aliases

No aliases for this group.

Splittings

FittingC3×Q8×3−1+2 ⋊ C3
SylowQ8 ⋊ #6911

Subgroups

subgroupG/H
center, socleC2×C3C3×C22⋊H(3,𝔽3)
commutator, cosocleC32×Q8C33
FrattiniC2×C32C32×A4
FittingC3×Q8×3−1+2C3
hypercenterC2×C3×3−1+2A4
hypocenterQ8#6911
LCSG ▷ C32×Q8 ▷ C3×Q8 ▷ Q8
UCSC1 ◁ C2×C3 ◁ C2×C33 ◁ C2×C3×3−1+2

278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Polycyclic presentation:

3^5,2^3|c^3=e^2,f^2=h,g^2=h,c^a=cd,d^a=de,f^a=fg,g^a=f,c^b=ce^2,g^f=gh

Conjugacy classes & character table

103 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 1652);