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#14279933

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

No aliases for this group.

Splittings

Fitting	C₂×C₃×C₄²×C₅ ⋊ C₄
Hall	C₃×C₅ ⋊ C₄⋊#95
Sylow	C₅ ⋊ #71535
Sylow	C₃ ⋊ #10604198

Subgroups

	subgroup	G/H
center, Frattini	C₂³	C₂²×ΓL(1,𝔽₁₆)
commutator	C₂²×C₃×C₅	C₂×C₄²
Fitting	C₂×C₃×C₄²×C₅	C₄
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical, cosocle	C₂³×C₃×D₅	C₂³
hypercenter	C₂×C₄²	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	C₄⋊#95
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

1312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 480

Polycyclic presentation:

2^7,3,5|a^2=f,b^2=g,c^2=e,b^a=bd,c^a=ce,h^a=h^2,i^a=i^2,i^f=i^4

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 5631);