C₅×#82013 #14478497

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₅×#82013

Splittings

Fitting	C₃×C₅×#504 ⋊ C₂
Hall	C₃×C₅ ⋊ #3415
Sylow	C₃ ⋊ C₅×#3415

Subgroups

	subgroup	G/H
center	C₂×C₅	C₂²×D₂₄
commutator, cosocle	C₃×C₈	C₂⁴×C₅
Frattini	C₈	C₂³×C₅×D₃
Fitting	C₃×C₅×#504	C₂
socle	C₂×C₃×C₅	C₂²×D₈
hypercenter	C₅×#504	D₃
hypocenter	C₃	C₅×#3415
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₅×#41 ◁ C₅×#131 ◁ C₅×#504

740 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 40 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 204195);

C5×#82013 #14478497