C₁₉×#1684 #14559541

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1665
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#1684

Subgroups

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

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

normal subgroups only

This group has 144 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) = 51
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,27)(22,28,31,35)(23,32,29,26)(25,33,34,30)(36,37)(38,44)(39,41)(40,48)(42,46)(43,47)(45,51)(49,50);(20,22,29,33,24,31,23,30)(21,25,32,35,27,34,26,28)(37,41)(42,50)(43,48)(44,51);(36,38,39,45)(37,42,41,50)(40,49,47,46)(43,51,48,44)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1684, C₁₉×#19123, C₁₉×#19126, …
maximal normal subgroup of	C₂×C₁₉×#1684, C₁₉×#19123, C₁₉×#19126, …
maximal quotient of	C₁₉×#8649, C₁₉×#9216, C₁₉×#9220, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 416);