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H(3,𝔽₃)×C₇₉⋊C₃ #20264256

order	6399
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₃⁴

Aliases

H(3,𝔽₃)×C₇₉⋊C₃

Splittings

Fitting	H(3,𝔽₃)×C₇₉ ⋊ C₃
Sylow	C₇₉ ⋊ C₃×H(3,𝔽₃)

Subgroups

	subgroup	G/H
center, Frattini	C₃	C₃²×C₇₉⋊C₃
commutator, socle	C₃×C₇₉	C₃³
Fitting	H(3,𝔽₃)×C₇₉	C₃
hypercenter	H(3,𝔽₃)	C₇₉⋊C₃
hypocenter	C₇₉	C₃×H(3,𝔽₃)
LCS	G ▷ C₃×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₃ ◁ H(3,𝔽₃)

112 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

319 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AΣL(1,𝔽₂₇)×C₇₉⋊C₃, #731×C₇₉⋊C₃, #732×C₇₉⋊C₃, …
maximal normal subgroup of	AΣL(1,𝔽₂₇)×C₇₉⋊C₃, #731×C₇₉⋊C₃, #732×C₇₉⋊C₃, …
maximal quotient of	C₃²⋊C₉×C₇₉⋊C₃, #34063238, H(3,𝔽₃)×C₇₉⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6399, 40);