C₅×#67820 #14278921

order	1920
isoclinism	isoclinic class of #4513
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#67820

Splittings

Hall	C₃×C₅ ⋊ #1385
Sylow	C₃ ⋊ C₅×#1385

Subgroups

	subgroup	G/H
center	C₄×C₅	#817
commutator	C₃×C₈	C₄²×C₅
Frattini	C₂²×C₈	C₂×C₅×D₃
Fitting	C₂×C₃×C₅×M₃₂	C₂
socle	C₂×C₃×C₅	#340
prime radical	C₂³×C₃×C₅	Q₁₆
cosocle	C₂²×C₃×C₈	C₂²×C₅
hypercenter	C₂×C₅×M₃₂	D₃
hypocenter	C₃	C₅×#1385
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×C₈ ◁ C₂×C₅×M₃₂

248 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 2 generators on 40 points:

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

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, 4619);