C₅×#68169 #14281852

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#68169

Splittings

Fitting	C₃×C₅×D₄⋊C₈ ⋊ C₂
Hall	C₃×C₅ ⋊ #1482
Sylow	C₃ ⋊ C₅×#1482

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×D₄⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#938	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×D₄⋊C₈	D₃
hypocenter	C₃	C₅×#1482
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄²×C₅ ◁ C₅×D₄⋊C₈

424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 960

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

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

Conjugacy classes & character table

330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 7550);

C5×#68169 #14281852