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C₂×(C₂×AGL(1,𝔽₅))⋊Dic₃ #11751983

order	960
isoclinism	isoclinic class of (C₂×D₃)⋊AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×(C₂×AGL(1,𝔽₅))⋊Dic₃

Splittings

Hall	C₃×C₅ ⋊ C₂×#95
Sylow	C₅ ⋊ C₂×C₃⋊#95
Sylow	C₃ ⋊ C₂×(C₂×AGL(1,𝔽₅))⋊C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂³	D₃×AGL(1,𝔽₅)
commutator	C₂×C₃×C₅	C₂×C₄²
Frattini	C₂²	C₂×D₃×AGL(1,𝔽₅)
Fitting, socle	C₂³×C₃×C₅	C₂×C₄
prime radical	C₂³×C₃×D₅	C₂²
cosocle	C₂²×C₃×D₅	C₂³
hypocenter	C₃×C₅	C₂×#95
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³

660 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 240

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₅)×C₃⋊#95, ΓL(1,𝔽₁₆)⋊#95, Dic₃×(C₂×AGL(1,𝔽₅))⋊C₄, …
maximal normal subgroup of	AGL(1,𝔽₅)×C₃⋊#95, ΓL(1,𝔽₁₆)⋊#95, Dic₃×(C₂×AGL(1,𝔽₅))⋊C₄, …
maximal quotient of	C₄×(C₂×AGL(1,𝔽₅))⋊Dic₃, #14279879, #14279880, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 6178);