C₁₉×#1387 #14559244

order	2432
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1387

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#102
commutator	C₈	C₄²×C₁₉
Frattini, cosocle	C₂²×C₈	C₂²×C₁₉
prime radical	C₂³×C₁₉	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

136 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 1216

A minimal faithful permutation representation — 2 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)(25,29)(26,33)(27,34)(30,32)(31,38)(35,39)(36,37);(24,25,26,30,34,36,39,37,28,32,35,29,27,31,33,38)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1387, C₁₉×#12569, C₄×C₁₉×#361, …
maximal normal subgroup of	C₂×C₁₉×#1387, C₁₉×#12569, C₄×C₁₉×#361, …
maximal quotient of	C₁₉×#7159, C₁₉×#7176, C₁₉×#7178, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 119);