C₁₉×#2140 #14559997

order	2432
nilpotency class	4
isoclinism	isoclinic class of #509
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#2140

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator	C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₂²×D₈×C₁₉	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

260 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 104 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)(20,21,22,23)(24,25)(26,31)(27,30)(28,37)(29,33)(32,35)(34,38)(36,39);(25,30)(26,28)(27,35)(31,32)(33,39)(34,36)(37,38);(24,26,29,28)(25,31,33,37)(27,34,36,35)(30,38,39,32)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12647, C₁₉×#12741, C₁₉×#12750, …
maximal normal subgroup of	C₁₉×#12647, C₁₉×#12741, C₁₉×#12750, …
maximal quotient of	C₁₉×#11593, C₁₉×#11649, C₁₉×#11661, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 872);