C₁₉×#2931 #14560788

order	2432
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#2931

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂³
commutator	C₂²	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂³×C₄
prime radical	C₁₉×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ G

500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 39 points:

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

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#8241, C₁₉×#8243, C₁₉×#8245, …
maximal normal subgroup of	C₁₉×#8241, C₁₉×#8243, C₁₉×#8245, …
maximal quotient of	C₁₉×#17956, C₁₉×#17957, C₁₉×#17958, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1663);

C19×#2931 #14560788