C₁₃×C₂²⋊D₁₉ #14520348

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

Aliases

direct product	C₁₃×C₂²⋊D₁₉
unambiguous semidirect product	C₂²⋊(C₁₃×D₁₉)

Splittings

Fitting	C₂²×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	C₂²×C₁₃×C₁₉	C₂
socle	C₂×C₁₃×C₁₉	C₂²
hypercenter	C₂²×C₁₃	D₁₉
hypocenter	C₁₉	D₄×C₁₃
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×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)(14,15,17,19,21,23,25,27,29,31,32,30,28,26,24,22,20,18,16)(34,36);(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)

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, 18);

C13×C22⋊D19 #14520348