C₁₉×D₅₂ #14520351

order	1976
isoclinism	isoclinic class of Dic₂₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₉×D₅₂
unambiguous semidirect product	C₄⋊(C₁₉×D₁₃)

Splittings

Fitting	C₄×C₁₃×C₁₉ ⋊ C₂
Hall	C₁₃×C₁₉ ⋊ D₄
Sylow	C₁₃ ⋊ D₄×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	C₂×C₁₃×C₁₉	C₂²
hypercenter	C₄×C₁₉	D₁₃
hypocenter	C₁₃	D₄×C₁₉
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₉ ◁ C₄×C₁₉

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 988

A minimal faithful permutation representation — 2 generators on 36 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);(21,23)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)

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, 21);

C19×D52 #14520351