C₅×#87518 #14511452

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

Aliases

direct product

C₅×#87518

Subgroups

	subgroup	G/H
center, socle	C₂×C₅	C₂×#1020
commutator, cosocle, hypocenter	#997	C₂²×C₅
Frattini	C₂	C₂×C₅×#1020
Fitting	C₅×#585	D₃
prime radical	C₅×#5950	C₂
hypercenter	C₄×C₅	#1020
LCS	G ▷ #997
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅

506 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 32 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) = 37
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 2 generators on 37 points:

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

Conjugacy classes & character table

115 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237150);