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H(3,𝔽₃)×C₄₃⋊C₉ #23782785

order	10449
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉ · Schur multiplier (H₂) = C₃⁴

Aliases

H(3,𝔽₃)×C₄₃⋊C₉

Splittings

C₄₃ ⋊ C₉×H(3,𝔽₃)

Subgroups

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₄₃⋊C₃
commutator	C₃×C₄₃	C₃²×C₉
Fitting, prime radical	C₃×H(3,𝔽₃)×C₄₃	C₃
socle, cosocle	C₃²×C₄₃	C₃³
hypercenter	C₃×H(3,𝔽₃)	C₄₃⋊C₃
hypocenter	C₄₃	C₉×H(3,𝔽₃)
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃×H(3,𝔽₃)

202 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

561 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#44532437, #44532442, #44532450, …
maximal normal subgroup of	#44532437, #44532442, #44532450, …
maximal quotient of	C₃²⋊C₉×C₄₃⋊C₉, #44532273, #44532280, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 169);