C₅×#69707 #14288140

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

Aliases

direct product

C₅×#69707

Splittings

Hall	C₃×C₅ ⋊ #1605
Sylow	C₃ ⋊ C₅×#1605

Subgroups

	subgroup	G/H
center	C₂²×C₅	#937
commutator, cosocle	C₂²×C₃×C₄	C₂³×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#395	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₅×#395	D₃
hypocenter	C₃	C₅×#1605
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#395

476 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 480

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

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

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 13838);