C₁₃×Dic₃₈ #14520344

order	1976
isoclinism	isoclinic class of Dic₃₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×Dic₃₈
unambiguous semidirect product	C₁₉⋊(Q₈×C₁₃)

Splittings

Hall	C₁₃×C₁₉ ⋊ Q₈
Sylow	C₁₉ ⋊ Q₈×C₁₃

Subgroups

	subgroup	G/H
center	C₂×C₁₃	C₂×D₁₉
commutator, cosocle	C₂×C₁₉	C₂²×C₁₃
Frattini	C₂	C₂×C₁₃×D₁₉
Fitting	C₄×C₁₃×C₁₉	C₂
socle, prime radical	C₂×C₁₃×C₁₉	C₂²
hypercenter	C₄×C₁₃	D₁₉
hypocenter	C₁₉	Q₈×C₁₃
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₁₃ ◁ C₄×C₁₃

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)(18,21,20,19)(22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40);(14,18,16,20)(15,19,17,21)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1976, 14);

C13×Dic38 #14520344