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AGL(1,𝔽₅)×#882 #14321406

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

AGL(1,𝔽₅)×#882

Splittings

Fitting	C₃×C₅×C₂²⋊C₄ ⋊ C₂×C₄
Hall	C₃×C₅ ⋊ C₄×#120
Sylow	C₅ ⋊ C₄×#882
Sylow	C₃ ⋊ AGL(1,𝔽₅)×#120

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃×AGL(1,𝔽₅)
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×C₂²⋊C₄	C₂×C₄
prime radical	D₅×#882	C₂
cosocle	C₂²×C₃×D₅	C₂⁴
hypercenter	C₂²⋊C₄	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₄×#120
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

2448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 120

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×AGL(1,𝔽₅)×#120, AGL(1,𝔽₅)×#4741, AGL(1,𝔽₅)×#64091
maximal normal subgroup of	D₃×AGL(1,𝔽₅)×#120, AGL(1,𝔽₅)×#4741
maximal quotient of	AGL(1,𝔽₅)×#4741, AGL(1,𝔽₅)×#4822, AGL(1,𝔽₅)×#4747, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 47104);