C₅×#71452 #14315183

order	1920
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₈ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#71452

Splittings

Fitting	C₃×C₅×#504 ⋊ C₂
Hall	C₃×C₅ ⋊ #2170
Sylow	C₃ ⋊ C₅×#2170

Subgroups

	subgroup	G/H
center	C₅×C₁₆	#67
commutator	C₃×C₄	C₂²×C₅×C₈
Frattini	C₂×C₈	C₂²×C₅×D₃
Fitting	C₃×C₅×#504	C₂
socle	C₂×C₃×C₅	C₈×D₄
prime radical	C₅×#950	C₄
cosocle	C₂×C₃×C₈	C₂³×C₅
hypercenter	C₅×#504	D₃
hypocenter	C₃	C₅×#2170
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₅×C₁₆ ◁ C₂×C₅×C₁₆ ◁ C₅×#504

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3,4,5)(6,7,8)(9,12,14,21,13,26,28,32,15,27,30,34,29,40,33,16)(10,11,18,23,19,24,36,38,20,25,37,39,17,22,35,31);(9,11)(10,16)(12,18)(13,24)(14,23)(15,25)(17,34)(19,21)(20,32)(22,29)(26,36)(27,37)(28,38)(30,39)(31,33)(35,40);(7,8)(9,10,14,18,13,19,28,36,15,20,30,37,29,17,33,35)(11,21,23,26,24,32,38,27,25,34,39,40,22,16,31,12)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 40881);

C5×#71452 #14315183