C₅×#84008 #14478549

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

Aliases

direct product

C₅×#84008

Splittings

Fitting	C₃×C₅×#576 ⋊ C₂
Hall	C₃×C₅ ⋊ #3416
Sylow	C₃ ⋊ C₅×#3416

Subgroups

	subgroup	G/H
center	C₂×C₅	C₂²×#213
commutator, cosocle	C₃×C₈	C₂⁴×C₅
Frattini	C₈	C₂³×C₅×D₃
Fitting	C₃×C₅×#576	C₂
socle	C₂×C₃×C₅	C₂²×D₈
hypercenter	C₅×#576	D₃
hypocenter	C₃	C₅×#3416
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₅×#41 ◁ C₅×#131 ◁ C₅×#576

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 204247);

C5×#84008 #14478549