Finite Group Databasebeta

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#127×C₃⋊ΓL(1,𝔽₁₆) #72231674

order	5760
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵×C₃×C₄

Aliases

#127×C₃⋊ΓL(1,𝔽₁₆)

Splittings

Fitting	C₃²×C₅×#127 ⋊ C₄
Hall	C₃²×C₅ ⋊ C₄×#127
Sylow	C₃² ⋊ AGL(1,𝔽₅)×#127
Sylow	C₅ ⋊ #127×C₃⋊Dic₃

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂³×C₃⋊ΓL(1,𝔽₁₆)
commutator, socle	C₂²×C₃²×C₅	C₂³×C₄
Fitting	C₃²×C₅×#127	C₄
prime radical	C₃²×D₅×#127	C₂
cosocle	C₂²×C₃²×D₅	C₂⁴
hypercenter	#127	C₃⋊ΓL(1,𝔽₁₆)
hypocenter	C₃²×C₅	C₄×#127
LCS	G ▷ C₂²×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₂² ◁ #127

5544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 720

Conjugacy classes & character table

294 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃⋊D₃×AGL(1,𝔽₅)×#127
maximal normal subgroup of	C₃⋊D₃×AGL(1,𝔽₅)×#127

GAP

Past the SmallGroups library coverage — no SmallGroups id.