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C₉⋊C₉×C₄₃⋊C₃ #23782775

order	10449
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉ · Schur multiplier (H₂) = C₃³

Aliases

C₉⋊C₉×C₄₃⋊C₃

Splittings

Fitting	C₄₃×C₉⋊C₉ ⋊ C₃
Sylow	C₄₃ ⋊ C₃×C₉⋊C₉

Subgroups

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₄₃⋊C₃
commutator	C₃×C₄₃	C₃²×C₉
Fitting	C₄₃×C₉⋊C₉	C₃
socle, cosocle	C₃²×C₄₃	C₃³
prime radical	C₃²×C₄₃⋊C₃	C₃²
hypercenter	C₉⋊C₉	C₄₃⋊C₃
hypocenter	C₄₃	C₃×C₉⋊C₉
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

561 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄₃⋊C₃×#6875, #44534448, C₄₃⋊C₃×#6881, …
maximal normal subgroup of	C₄₃⋊C₃×#6875, #44534448, C₄₃⋊C₃×#6881, …
maximal quotient of	C₄₃⋊C₃×#6855, #44532240, C₉⋊C₉×C₄₃⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 159);