C₅×#70690 #14314040

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅×#70690

Splittings

Fitting	C₂×C₃×C₅×#108 ⋊ C₂
Hall	C₃×C₅ ⋊ #2143
Sylow	C₃ ⋊ C₅×#2143

Subgroups

	subgroup	G/H
center	C₄×C₅	C₂×#213
commutator	C₃×C₈	C₂²×C₄×C₅
Frattini	C₂×C₈	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×#108	C₂
socle	C₂×C₃×C₅	C₂×#102
prime radical	C₂×C₅×#904	C₂
cosocle	C₂×C₃×C₈	C₂³×C₅
hypercenter	C₂×C₅×#108	D₃
hypocenter	C₃	C₅×#2143
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×C₈ ◁ C₂×C₅×#108

440 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)(11,21)(16,31)(20,36)(22,38)(23,30)(25,40)(32,33)(34,37);(7,8)(9,11)(10,16)(12,25)(13,23)(14,30)(15,21)(17,34)(18,32)(19,31)(20,24)(22,27)(26,38)(28,40)(29,33)(35,37)(36,39);(9,10,13,18,15,19,14,29)(11,20,23,37,21,36,30,34)(12,24,26,35,28,39,27,17)(16,25,32,38,31,40,33,22)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 39738);

C5×#70690 #14314040