C₅×#71445 #14313971

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

Aliases

direct product

C₅×#71445

Splittings

Hall	C₃×C₅ ⋊ #2141
Sylow	C₃ ⋊ C₅×#2141

Subgroups

	subgroup	G/H
center	C₂²×C₅	C₂×D₂₄
commutator	C₃×C₈	C₂²×C₄×C₅
Frattini	C₂×C₈	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×M₃₂	C₂
socle	C₂²×C₃×C₅	C₂×D₈
prime radical	C₂³×C₃×C₅	D₈
cosocle	C₂×C₃×C₈	C₂³×C₅
hypercenter	C₂×C₅×M₃₂	D₃
hypocenter	C₃	C₅×#2141
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×C₈ ◁ C₂×C₅×M₃₂

440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 44 points:

(1,2,3,4,5)(6,7,8)(13,16,19,18)(14,21,23,34)(15,25,28,27)(17,29,33,32)(20,35,36,37)(22,30,39,40)(24,38,41,44)(26,42,43,31);(7,8)(13,15,19,28)(14,20,23,36)(16,27,18,25)(17,31,33,42)(21,37,34,35)(22,38,39,44)(24,40,41,30)(26,29,43,32);(7,8)(9,10,11,12)(13,14)(15,24)(16,21)(17,30)(18,34)(19,23)(20,26)(22,32)(25,38)(27,44)(28,41)(29,39)(31,37)(33,40)(35,42)(36,43)

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, 39669);

C5×#71445 #14313971