C₅×#70777 #14284739

order	1920
isoclinism	isoclinic class of #4451
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#70777

Splittings

Hall	C₃×C₅ ⋊ #1544
Sylow	C₃ ⋊ C₅×#1544

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅	(C₂×D₃)⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#431	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂³×C₃×C₅	C₂²⋊C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#431	D₃
hypocenter	C₃	C₅×#1544
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₅×#431

404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 40 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 10437);

C5×#70777 #14284739