C₅×#73029 #14510753

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

Aliases

direct product

C₅×#73029

Subgroups

	subgroup	G/H
center, socle, hypercenter	C₂×C₅	#1020⋊C₂
commutator, cosocle, hypocenter	#997	C₂²×C₅
Frattini	C₂³	C₂×C₅×S₄
Fitting	C₅×#458	D₃
prime radical	C₅×#997	C₂²
LCS	G ▷ #997
UCS	C₁ ◁ C₂×C₅

224 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 22 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)(6,17,21,19,9,33,11,20,34,8,22,32)(7,25,28,16,13,36,15,27,37,12,29,35)(10,23,24,18)(14,30,31,26);(6,7,11,15)(8,16,19,12)(9,14,22,31)(10,13,24,29)(17,30,20,26)(18,27,23,25)(21,28,34,37)(32,36,33,35)

Conjugacy classes & character table

85 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236451);