C₅×#67818 #14278905

order	1920
isoclinism	isoclinic class of #4513
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₅×#67818

Splittings

Hall	C₃×C₅ ⋊ #1384
Sylow	C₃ ⋊ C₅×#1384

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	D₈
cosocle	C₂²×C₃×C₈	C₂²×C₅
hypercenter	C₂×C₅×M₃₂	D₃
hypocenter	C₃	C₅×#1384
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×C₈ ◁ C₂×C₅×M₃₂

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

normal subgroups only

This group has 264 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)(9,11,13,24,29,38,27,36,15,23,26,37,14,25,12,22)(10,16,18,32,30,39,17,21,20,31,34,40,19,33,28,35);(7,8)(9,10)(11,21,23,35)(12,18)(13,28)(14,30)(15,20)(16,22,31,36)(17,26)(19,29)(24,39,37,33)(25,40,38,32)(27,34)

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, 4603);