C₅×#72986 #14510710

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

solvable

Aliases

direct product

C₅×#72986

Subgroups

	subgroup	G/H
center	C₂×C₅	C₂×#857
commutator, cosocle, hypocenter	#95⋊C₃	C₂²×C₅
Frattini	C₂³	C₂×C₅×S₄
Fitting	C₅×#376	D₃
socle	C₂³×C₅	C₂×S₄
prime radical	C₅×#95⋊C₃	C₂²
hypercenter	C₄×C₅	#857
LCS	G ▷ #95⋊C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅

208 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 26 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) = 49
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 2 generators on 49 points:

(1,2,3,4,5)(6,7,17)(8,13,11)(9,14,16)(10,12,15)(18,45,33,31,34,46,23,29,36,20,21,44)(19,42,40,28,35,49,27,38,41,24,25,48)(22,30,37,47)(26,39,32,43);(7,11)(12,16)(13,15)(14,17)(18,19,23,27)(20,28,31,24)(21,32,34,26)(22,35,37,25)(29,39,45,43)(30,38,47,42)(33,41,36,40)(44,48,46,49)

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236408);