C₅×#79895 #14458230

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₅×#79895

Splittings

Fitting	C₃×C₅×#443 ⋊ C₂
Hall	C₃×C₅ ⋊ #3293
Sylow	C₃ ⋊ C₅×#3293

Subgroups

	subgroup	G/H
center	C₂×C₅	D₄×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#443	C₂
socle	C₂×C₃×C₅	D₄²
hypercenter	C₅×#443	D₃
hypocenter	C₃	C₅×#3293
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#443

888 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 4 generators on 40 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 183928);

C5×#79895 #14458230