C₅×#86132 #14495594

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₅×#86132

Splittings

Fitting	C₃×C₅×#529 ⋊ C₂
Hall	C₃×C₅ ⋊ #3531
Sylow	C₃ ⋊ C₅×#3531

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#529	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#529	D₃
hypocenter	C₃	C₅×#3531
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#529

1860 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 5 generators on 40 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 221292);

C5×#86132 #14495594