C₁₉×#1057 #14520335

order	1976
isoclinism	isoclinic class of #261
automorphism	?
homology	Abelianization (H₁) = C₈×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₉×#1057

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	#261
commutator, hypocenter	C₁₃	C₈×C₁₉
Frattini	C₂	C₁₉×#261
Fitting, socle, prime radical	C₂×C₁₃×C₁₉	C₄
cosocle	Dic₁₃	C₂×C₁₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₉

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:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,22,23,25)(24,27,28,32)(26,30,31,29)(33,34,35,37,36,38,39,40);(20,21,24,27,31,25,29,30,22,26,32,28,23)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1976, 5);

C19×#1057 #14520335