C₁₃×Dic₂₀ #11760127

order	1040
isoclinism	isoclinic class of #677
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₃×Dic₂₀

Splittings

Hall	C₅×C₁₃ ⋊ Q₁₆
Sylow	C₅ ⋊ C₁₃×Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₁₃	D₂₀
commutator, cosocle	C₄×C₅	C₂²×C₁₃
Frattini	C₄	C₂×D₅×C₁₃
Fitting	C₅×C₈×C₁₃	C₂
socle, prime radical	C₂×C₅×C₁₃	D₄
hypercenter	C₈×C₁₃	D₅
hypocenter	C₅	C₁₃×Q₁₆
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₃ ◁ C₄×C₁₃ ◁ C₈×C₁₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 1040

A minimal faithful permutation representation — 2 generators on 34 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1040, 56);

C13×Dic20 #11760127