D₂₀×C₄₉ #14519924

order	1960
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₂₀×C₄₉
unambiguous semidirect product	C₄⋊(D₅×C₄₉)

Splittings

Fitting	C₄×C₅×C₄₉ ⋊ C₂
Hall	C₅×C₄₉ ⋊ D₄
Sylow	C₅ ⋊ D₄×C₄₉

Subgroups

	subgroup	G/H
center	C₂×C₄₉	C₂×D₅
commutator	C₂×C₅	C₂²×C₄₉
Frattini	C₂×C₇	C₂×C₇×D₅
Fitting	C₄×C₅×C₄₉	C₂
socle, cosocle	C₂×C₅×C₇	C₂²×C₇
prime radical	C₇×D₂₀	C₇
hypercenter	C₄×C₄₉	D₅
hypocenter	C₅	D₄×C₄₉
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄₉ ◁ C₄×C₄₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 58
transitive degree	μ_t(G) = 980

A minimal faithful permutation representation — 2 generators on 58 points:

(1,2,3,4)(5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58);(2,4)(6,9)(7,8)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 21);

D20×C49 #14519924