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SL(2,𝔽₃)×C₉⋊C₉ #14517191

order	1944
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉ · Schur multiplier (H₂) = C₃³

solvable

Aliases

SL(2,𝔽₃)×C₉⋊C₉

Splittings

Fitting	Q₈×C₉⋊C₉ ⋊ C₃
Sylow	Q₈ ⋊ C₃×C₉⋊C₉

Subgroups

	subgroup	G/H
center, Frattini, socle	C₂×C₃²	C₃²×A₄
commutator	C₃×Q₈	C₃²×C₉
Fitting	Q₈×C₉⋊C₉	C₃
prime radical	C₃²×SL(2,𝔽₃)	C₃²
cosocle	C₃²×Q₈	C₃³
hypercenter	C₂×C₉⋊C₉	A₄
hypocenter	Q₈	C₃×C₉⋊C₉
LCS	G ▷ C₃×Q₈ ▷ Q₈
UCS	C₁ ◁ C₂×C₃² ◁ C₂×C₉⋊C₉

287 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 648

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	SL(2,𝔽₃)×#6875, C₉⋊C₉×#997, #72276184
maximal normal subgroup of	SL(2,𝔽₃)×#6875
maximal quotient of	SL(2,𝔽₃)×#6875

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 1585);