C₅×#71656 #14302986

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₅×#71656

Splittings

Fitting	C₃×C₅×#518 ⋊ C₂
Hall	C₃×C₅ ⋊ #1913
Sylow	C₃ ⋊ C₅×#1913

Subgroups

	subgroup	G/H
center	C₂×C₅	#5213
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂⁴	C₂²×C₅×D₃
Fitting	C₃×C₅×#518	C₂
socle	C₂×C₃×C₅	#386
prime radical	C₅×#5804	C₂
cosocle	C₂⁴×C₃	C₂³×C₅
hypercenter	C₅×#518	D₃
hypocenter	C₃	C₅×#1913
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂⁴×C₅ ◁ C₅×#518

760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 28684);

C5×#71656 #14302986