C₅×#69067 #14315632

order	1920
isoclinism	isoclinic class of D₄₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#69067

Splittings

Fitting	C₃×C₄×C₅×C₁₆ ⋊ C₂
Hall	C₃×C₅ ⋊ #2178
Sylow	C₃ ⋊ C₅×#2178

Subgroups

	subgroup	G/H
center	C₅×C₈	D₂₄
commutator	C₃×C₈	C₂²×C₄×C₅
Frattini	C₂×C₈	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×C₁₆	C₂
socle	C₂×C₃×C₅	C₄×D₈
prime radical	C₅×#4904	C₂
cosocle	C₂×C₃×C₈	C₂³×C₅
hypercenter	C₄×C₅×C₁₆	D₃
hypocenter	C₃	C₅×#2178
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₅×C₈ ◁ C₂×C₅×C₈ ◁ C₄×C₅×C₈ ◁ C₄×C₅×C₁₆

292 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)(6,7,8)(9,12,14,26,15,27,30,13)(10,17,18,35,20,36,19,28)(11,22,23,31,25,39,24,29)(16,32,33,38,34,40,37,21);(7,8)(9,11)(10,16)(12,22)(13,29)(14,23)(15,25)(17,32)(18,33)(19,37)(20,34)(21,28)(24,30)(26,31)(27,39)(35,38)(36,40);(7,8)(9,10,14,18,15,20,30,19)(11,21,23,32,25,38,24,40)(12,17,26,35,27,36,13,28)(16,31,33,39,34,29,37,22)

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, 41330);

C5×#69067 #14315632