C₅×#78706 #14412198

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₅ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₅×#78706

Splittings

Fitting	C₂×C₃×C₅×#101 ⋊ C₂
Hall	C₃×C₅ ⋊ #2889
Sylow	C₃ ⋊ C₅×#2889

Subgroups

	subgroup	G/H
center	C₂×C₅	C₂×D₃×C₂²⋊C₄
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#101	C₂
socle	C₂×C₃×C₅	C₂²×C₂²⋊C₄
prime radical	C₂×C₅×#1007	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×#101	D₃
hypocenter	C₃	C₅×#2889
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#101

1408 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)(12,23)(16,29)(20,34)(24,36)(27,33)(30,39)(35,37)(38,40);(7,8)(9,12)(10,16)(11,20)(13,24)(14,23)(15,27)(17,29)(18,30)(19,33)(21,35)(22,34)(25,37)(26,36)(28,38)(31,39)(32,40);(9,11,14,22)(10,15,17,19)(12,20,23,34)(13,25,26,21)(16,27,29,33)(18,32,31,28)(24,37,36,35)(30,40,39,38);(9,10,13,18,14,17,26,31)(11,19,21,32,22,15,25,28)(12,16,24,30,23,29,36,39)(20,33,35,40,34,27,37,38)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137896);

C5×#78706 #14412198