C₅×#69377 #14319239

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#69377

Splittings

Fitting	C₃×C₅×D₃₂ ⋊ C₂
Hall	C₃×C₅ ⋊ #2263
Sylow	C₃ ⋊ C₅×#2263

Subgroups

	subgroup	G/H
center	C₂×C₅	D₃×D₁₆
commutator, cosocle	C₃×C₁₆	C₂³×C₅
Frattini	C₁₆	C₂²×C₅×D₃
Fitting	C₃×C₅×D₃₂	C₂
socle	C₂×C₃×C₅	C₂×D₁₆
hypercenter	C₅×D₃₂	D₃
hypocenter	C₃	C₅×#2263
LCS	G ▷ C₃×C₁₆ ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×C₁₆ ◁ C₅×D₃₂

224 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 40
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 3 generators on 40 points:

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

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, 44937);