C₅×#67650 #14278143

order	1920
isoclinism	isoclinic class of #67645
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅×#67650

Splittings

Hall	C₃×C₅ ⋊ #1346
Sylow	C₃ ⋊ C₅×#1346

Subgroups

	subgroup	G/H
center	C₂²×C₅	#834
commutator	C₂²×C₃×C₄	C₂×C₄×C₅
Frattini	C₂×C₄⋊C₄	C₂×C₅×D₃
Fitting	C₃×C₅×#398	C₂
socle	C₂²×C₃×C₅	#99
prime radical	C₂³×C₃×C₅	C₂²⋊C₄
cosocle	C₂×C₃×C₄⋊C₄	C₂²×C₅
hypercenter	C₅×#398	D₃
hypocenter	C₃	C₅×#1346
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₅ ◁ C₂×C₅×C₄⋊C₄ ◁ C₅×#398

248 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 74 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 — 2 generators on 32 points:

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

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, 3841);