C₅×#67574 #14278552

order	1920
isoclinism	isoclinic class of #67573
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×#67574

Splittings

Hall	C₃×C₅ ⋊ #1366
Sylow	C₃ ⋊ C₅×#1366

Subgroups

	subgroup	G/H
center	C₂×C₅	#4481
commutator	C₃×C₄²	C₂×C₄×C₅
Frattini	C₄×C₈	C₂×C₅×D₃
Fitting	C₃×C₅×#364	C₂
socle	C₂×C₃×C₅	#333
prime radical	C₂²×C₃×C₅	#100
cosocle	C₃×C₄×C₈	C₂²×C₅
hypercenter	C₅×#364	D₃
hypocenter	C₃	C₅×#1366
LCS	G ▷ C₃×C₄² ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₄×C₅×C₈ ◁ C₅×#364

148 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 70 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)(9,11,14,21)(10,15)(12,24,27,29)(13,28,25,23)(16,20)(17,33)(18,37)(19,31)(22,26,38,36)(30,34)(32,39)(35,40);(7,8)(9,10,12,17,25,18,36,34,14,19,27,35,13,16,26,32)(11,20,22,33,28,31,24,39,21,37,38,40,23,15,29,30)

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4250);