C₁₉×#1693 #14559550

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1685
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₉×#1693

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₁₉
prime radical	C₂×D₄×C₁₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

166 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 35
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12378, C₁₉×#12379, C₁₉×#12402, …
maximal normal subgroup of	C₁₉×#12378, C₁₉×#12379, C₁₉×#12402, …
maximal quotient of	C₁₉×#8652, C₁₉×#9225, C₁₉×#9573, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 425);