Dic₁₀×C₄₉ #14519922

order	1960
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₁₀×C₄₉
unambiguous semidirect product	C₅⋊(Q₈×C₄₉)

Splittings

Hall	C₅×C₄₉ ⋊ Q₈
Sylow	C₅ ⋊ Q₈×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, prime radical, cosocle	C₂×C₅×C₇	C₂²×C₇
hypercenter	C₄×C₄₉	D₅
hypocenter	C₅	Q₈×C₄₉
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄₉ ◁ C₄×C₄₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 62
transitive degree	μ_t(G) = 1960

A minimal faithful permutation representation — 2 generators on 62 points:

(1,2,3,4)(5,8,7,6)(9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62);(1,5,3,7)(2,6,4,8)(10,13)(11,12)

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, 19);

Dic10×C49 #14519922