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C₅×#71044 #14289874

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

Aliases

Splittings

Fitting	C₃×C₅×#461 ⋊ C₂
Hall	C₃×C₅ ⋊ #1639
Sylow	C₃ ⋊ C₅×#1639

Subgroups

	subgroup	G/H
center	C₂²×C₅	#937
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#461	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₅×D₄×D₁₂	C₂
hypercenter	C₅×#461	D₃
hypocenter	C₃	C₅×#1639
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#461

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 480

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

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

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 15572);