C₅×#71372 #14291763

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

Aliases

direct product

C₅×#71372

Splittings

Fitting	C₃×C₅×#500 ⋊ C₂
Hall	C₃×C₅ ⋊ #1675
Sylow	C₃ ⋊ C₅×#1675

Subgroups

	subgroup	G/H
center	C₂²×C₅	#938
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#500	C₂
socle	C₂²×C₃×C₅	#121
prime radical	C₂×C₅×D₁₂	D₄
hypercenter	C₅×#500	D₃
hypocenter	C₃	C₅×#1675
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#500

320 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 32
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 32 points:

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

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, 17461);