C₁₃×C₁₉⋊C₈ #14520332

order	1976
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₈×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₁₉⋊C₈
unambiguous semidirect product	C₁₉⋊(C₈×C₁₃)

Splittings

derived, Sylow	C₁₉ ⋊ C₈×C₁₃
Hall	C₁₃×C₁₉ ⋊ C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₁₃	D₁₉
commutator, hypocenter	C₁₉	C₈×C₁₃
Frattini	C₄	C₁₃×D₁₉
Fitting	C₄×C₁₃×C₁₉	C₂
socle, prime radical	C₂×C₁₃×C₁₉	C₄
cosocle	C₄×C₁₉	C₂×C₁₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₄×C₁₃

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1976, 2);

C13×C19⋊C8 #14520332