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C₅×#68444 #14291973

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂

Aliases

Splittings

Fitting	C₃×C₅×#332 ⋊ C₂
Hall	C₃×C₅ ⋊ #1679
Sylow	C₃ ⋊ C₅×#1679

Subgroups

	subgroup	G/H
center	C₂²×C₅	#884
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#332	C₂
socle	C₂²×C₃×C₅	#121
prime radical	C₂×C₅×D₁₂	D₄
hypercenter	C₅×#332	D₃
hypocenter	C₃	C₅×#1679
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#332

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3,4,5)(6,7)(10,14)(12,16)(13,15);(7,8)(10,13)(14,15)(17,19,20,18,21,22,24,23);(9,10)(11,13)(12,14)(15,16)(17,18,21,23)(19,24,22,20)

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 17671);