C₅×#69087 #14312746

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#69087

Splittings

Fitting	C₃×C₅×#347 ⋊ C₂
Hall	C₃×C₅ ⋊ #2110
Sylow	C₃ ⋊ C₅×#2110

Subgroups

	subgroup	G/H
center	C₄×C₅	C₄²×D₃
commutator	C₃×C₄	C₂×C₄²×C₅
Frattini	C₂×C₈	C₂²×C₅×D₃
Fitting	C₃×C₅×#347	C₂
socle	C₂×C₃×C₅	C₂×#97
prime radical	C₂²×C₅×D₃	M₁₆
cosocle	C₂×C₃×C₈	C₂³×C₅
hypercenter	C₅×#347	D₃
hypocenter	C₃	C₅×#2110
LCS	G ▷ C₃×C₄ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₅×#347

320 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)(7,8)(11,20)(15,28)(19,34)(21,23)(22,36)(27,37)(29,30)(35,38);(6,7,8)(9,11)(10,15,17,28)(12,23)(13,22)(14,20)(16,30,31,29)(18,19,33,34)(21,25)(24,27)(26,36)(32,38,40,35)(37,39);(9,10,12,16,13,18,24,32,14,17,25,31,26,33,39,40)(11,19,21,35,22,28,37,30,20,34,23,38,36,15,27,29)

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, 38444);

C5×#69087 #14312746