C₁₉×#2880 #14560737

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#2880

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂³×C₄
prime radical	C₂²×#41×C₁₉	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 608

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

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9239, C₁₉×#9241, C₁₉×#9345, …
maximal normal subgroup of	C₁₉×#9239, C₁₉×#9241, C₁₉×#9345, …
maximal quotient of	C₁₉×#17411, C₁₉×#17412, C₁₉×#17413, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1612);

C19×#2880 #14560737

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#2880 #14560737