C₅×#82012 #14478157

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅×C₈ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₅×#82012

Splittings

Fitting	C₃×C₅×#504 ⋊ C₂
Hall	C₃×C₅ ⋊ #3407
Sylow	C₃ ⋊ C₅×#3407

Subgroups

	subgroup	G/H
center	C₅×C₈	C₂³×D₃
commutator	C₂×C₃	C₂³×C₅×C₈
Frattini	C₈	C₂³×C₅×D₃
Fitting	C₃×C₅×#504	C₂
socle	C₂×C₃×C₅	C₂³×C₈
prime radical	C₅×D₃×#41	C₄
cosocle	C₃×C₈	C₂⁴×C₅
hypercenter	C₅×#504	D₃
hypocenter	C₃	C₅×#3407
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₅×C₈ ◁ C₅×#504

720 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)(7,8)(10,16)(15,25)(17,28)(18,29)(26,35)(27,36)(30,38)(37,40);(6,7,8)(11,19)(15,25)(20,31)(21,32)(26,35)(27,36)(33,39)(37,40);(9,11)(10,15)(12,20)(13,21)(14,19)(16,25)(17,26)(18,27)(22,33)(23,31)(24,32)(28,35)(29,36)(30,37)(34,39)(38,40);(9,10,12,17,13,18,22,30,14,16,23,28,24,29,34,38)(11,15,20,26,21,27,33,37,19,25,31,35,32,36,39,40)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 203855);

C5×#82012 #14478157