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(C3×C127⋊C3)⋊H(3,𝔽3) #44525023

order30861
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C36

Aliases

unambiguous semidirect product(C3×C127⋊C3)⋊H(3,𝔽3)

Splittings

FittingC3×H(3,𝔽3)×C127 ⋊ C3
SylowC127 ⋊ C32⋊H(3,𝔽3)

Subgroups

subgroupG/H
center, FrattiniC32C32×C127⋊C3
commutator, socle, cosocleC32×C127C33
FittingC3×H(3,𝔽3)×C127C3
hypercenterC3×H(3,𝔽3)C127⋊C3
hypocenterC127C32⋊H(3,𝔽3)
LCSG ▷ C32×C127 ▷ C127
UCSC1 ◁ C32 ◁ C3×H(3,𝔽3)

378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3429

Polycyclic presentation:

3^5,127|b^a=bd,c^a=ce,f^c=f^107

Conjugacy classes & character table

1437 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30861, 177);