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D₃×D₅⋊M₃₂ #14478107

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product	D₃×D₅⋊M₃₂
unambiguous semidirect product	D₅⋊(D₃×M₃₂)
unambiguous semidirect product	(D₃×D₅)⋊M₃₂

Splittings

Hall	C₃×C₅ ⋊ C₂²×M₃₂
Sylow	C₅ ⋊ C₂×D₃×M₃₂
Sylow	C₃ ⋊ C₂×D₅⋊M₃₂

Subgroups

	subgroup	G/H
center	C₈	C₂×D₃×AGL(1,𝔽₅)
commutator, socle	C₂×C₃×C₅	C₂³×C₈
Frattini	C₄	C₂²×D₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
prime radical	C₂²×D₃×D₅	C₈
cosocle	C₃×#168	C₂⁴
hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₂²×M₃₂
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₈ ◁ C₂×C₈

800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 240

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 203805);