C₅×#70040 #14295508

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₅ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₅×#70040

Splittings

Hall	C₃×C₅ ⋊ #1757
Sylow	C₃ ⋊ C₅×#1757

Subgroups

	subgroup	G/H
center	C₄×C₅	D₃×C₂²⋊C₄
commutator	C₂²×C₃	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#410	C₂
socle	C₂×C₃×C₅	C₄×C₂²⋊C₄
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#410	D₃
hypocenter	C₃	C₅×#1757
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#410

568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

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, 21206);

C5×#70040 #14295508