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#120×PSU(3,𝔽₂) #72220409

order	2304
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰×C₃

Aliases

#120×PSU(3,𝔽₂)

Splittings

Fitting	C₃²×#120 ⋊ Q₈
Sylow	C₃² ⋊ Q₈×#120

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂³×PSU(3,𝔽₂)
commutator, cosocle	C₂²×C₃⋊D₃	C₂⁵
Fitting	C₃²×#120	Q₈
socle	C₂²×C₃²	C₂³×Q₈
prime radical	C₃⋊D₃×#120	C₂²
hypercenter	#120	PSU(3,𝔽₂)
hypocenter	C₃²	Q₈×#120
LCS	G ▷ C₂²×C₃⋊D₃ ▷ C₃²
UCS	C₁ ◁ C₂² ◁ #120

5497 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#120×PSU(3,𝔽₂)⋊C₃, #120×AΓL(1,𝔽₉), B(4,𝔽₂)×PSU(3,𝔽₂), …
maximal normal subgroup of	#120×PSU(3,𝔽₂)⋊C₃, #120×AΓL(1,𝔽₉), B(4,𝔽₂)×PSU(3,𝔽₂), …
maximal quotient of	B(4,𝔽₂)×PSU(3,𝔽₂), #453×PSU(3,𝔽₂)

GAP

Past the SmallGroups library coverage — no SmallGroups id.