C₅×#71799 #14284456

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₅×#71799

Splittings

Hall	C₃×C₅ ⋊ #1536
Sylow	C₃ ⋊ C₅×#1536

Subgroups

	subgroup	G/H
center	C₂²×C₅	C₂×#217
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting, prime radical	C₃×C₅×#532	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#532	D₃
hypocenter	C₃	C₅×#1536
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ C₅×#532

476 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3,4,5)(6,7,8)(17,20,22,21)(18,24,25,29)(19,27,28,30)(23,31,32,26);(10,13)(11,15)(17,19)(18,23)(20,27)(21,30)(22,28)(24,31)(25,32)(26,29);(7,8)(9,10,11,14,12,13,15,16)(17,18)(19,26,28,31)(20,29)(21,24)(22,25)(23,27,32,30)

Conjugacy classes & character table

270 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 10154);

C5×#71799 #14284456