C₁₃×D₇₆ #14520346

order	1976
isoclinism	isoclinic class of Dic₃₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×D₇₆
unambiguous semidirect product	C₄⋊(C₁₃×D₁₉)

Splittings

Fitting	C₄×C₁₃×C₁₉ ⋊ C₂
Hall	C₁₃×C₁₉ ⋊ D₄
Sylow	C₁₉ ⋊ D₄×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	C₂×C₁₃×C₁₉	C₂²
hypercenter	C₄×C₁₃	D₁₉
hypocenter	C₁₉	D₄×C₁₃
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₁₃ ◁ C₄×C₁₃

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);(15,17)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)

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, 16);

C13×D76 #14520346