C₁₉×#2368 #14560225

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#2368

Subgroups

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

548 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)(20,21,23,22)(24,25)(26,29)(27,28)(30,31)(32,33,36,37)(34,38,39,35);(20,22,23,21)(25,28)(29,31)(33,37)(35,38);(24,26,27,30)(25,29,28,31)(32,34)(33,35)(36,39)(37,38);(24,25)(26,29)(27,28)(30,31)(32,35)(33,34)(36,38)(37,39)

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9276, C₁₉×#9278, C₂×C₁₉×#2368, …
maximal normal subgroup of	C₁₉×#9276, C₁₉×#9278, C₂×C₁₉×#2368, …
maximal quotient of	C₁₉×#13802, C₁₉×#13814, C₁₉×#13819, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1100);

C19×#2368 #14560225

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#2368 #14560225