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#95⋊H(3,𝔽3) #11720340

order864
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C2×C32

Aliases

unambiguous semidirect product#95⋊H(3,𝔽3)
unambiguous semidirect product(C3×#95⋊C3)⋊C3

Splittings

FittingC32×#95 ⋊ C3
Sylow#95 ⋊ H(3,𝔽3)

Subgroups

subgroupG/H
centerC2×C3C3×C42⋊C3
commutator, cosocleC3×#95C32
Frattini, socleC23×C3C3×A4
FittingC32×#95C3
hypercenterC2×C32C42⋊C3
hypocenter#95H(3,𝔽3)
LCSG ▷ C3×#95 ▷ #95
UCSC1 ◁ C2×C3 ◁ C2×C32

121 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36

Polycyclic presentation:

3^3,2^5|d^2=g,e^2=f,b^a=bc,d^a=de,e^a=dfh,f^a=g,g^a=fgh,e^d=eh

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

derived subgroup of#13136781, #13136782
maximal subgroup of(C3⋊#4621)⋊C3, (C3⋊#4622)⋊C3, #13136781, …
maximal normal subgroup of(C3⋊#4621)⋊C3, (C3⋊#4622)⋊C3, #13136781, …
maximal quotient of#338⋊H(3,𝔽3), C2×#95⋊H(3,𝔽3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 307);