C₁₉×#2063 #14559920

order	2432
nilpotency class	3
isoclinism	isoclinic class of #2018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#2063

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

228 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2063, C₁₉×#23601, C₁₉×#23602, …
maximal normal subgroup of	C₂×C₁₉×#2063, C₁₉×#23601, C₁₉×#23602, …
maximal quotient of	C₁₉×#10587, C₁₉×#10589, C₁₉×#10591, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 795);