C₁₉×Dic₂₆ #14520349

order	1976
isoclinism	isoclinic class of Dic₂₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×Dic₂₆
unambiguous semidirect product	C₁₃⋊(Q₈×C₁₉)

Splittings

Hall	C₁₃×C₁₉ ⋊ Q₈
Sylow	C₁₃ ⋊ Q₈×C₁₉

Subgroups

	subgroup	G/H
center	C₂×C₁₉	C₂×D₁₃
commutator, cosocle	C₂×C₁₃	C₂²×C₁₉
Frattini	C₂	C₂×C₁₉×D₁₃
Fitting	C₄×C₁₃×C₁₉	C₂
socle, prime radical	C₂×C₁₃×C₁₉	C₂²
hypercenter	C₄×C₁₉	D₁₃
hypocenter	C₁₃	Q₈×C₁₉
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₉ ◁ C₄×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 1976

A minimal faithful permutation representation — 2 generators on 40 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1976, 19);

C19×Dic26 #14520349