C₅×#73291 #14511015

order	1920
automorphism	?
homology	Abelianization (H₁) = C₃×C₅ · Schur multiplier (H₂) = C₂

solvable

Aliases

direct product

C₅×#73291

Splittings

Fitting, Hall	C₅×#2811 ⋊ C₃
derived, Sylow	#2811 ⋊ C₃×C₅

Subgroups

	subgroup	G/H
center, socle, hypercenter	C₂³×C₅	C₂²⋊A₄
commutator, cosocle, hypocenter	#2811	C₃×C₅
Frattini	C₂³	C₅×C₂²⋊A₄
Fitting	C₅×#2811	C₃
LCS	G ▷ #2811
UCS	C₁ ◁ C₂³×C₅

284 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 29
transitive degree	μ_t(G) = 640

A minimal faithful permutation representation — 3 generators on 29 points:

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

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236713);