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#49144382

order36693
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C32

Aliases

No aliases for this group.

Splittings

FittingC3×H(3,𝔽3)×C151 ⋊ C3
SylowC151 ⋊ #6856

Subgroups

subgroupG/H
centerC32C32⋊(C151⋊C3)
commutator, cosocleC33×C151C32
FrattiniC33C3×C151⋊C3
FittingC3×H(3,𝔽3)×C151C3
socleC32×C151H(3,𝔽3)
hypercenterC3×H(3,𝔽3)C151⋊C3
hypocenterC151#6856
LCSG ▷ C33×C151 ▷ C32×C151 ▷ C151
UCSC1 ◁ C32 ◁ C33 ◁ C3×H(3,𝔽3)

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12231

Polycyclic presentation:

3^5,151|b^a=bc,c^a=cd,c^b=ce,f^b=f^32

Conjugacy classes & character table

1685 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36693, 70);