C₁₉×#1389 #14559246

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

Aliases

direct product

C₁₉×#1389

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#102
commutator	C₈	C₄²×C₁₉
Frattini, cosocle	C₂²×C₈	C₂²×C₁₉
socle	C₂×C₁₉	#340
prime radical	C₂³×C₁₉	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

128 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 76 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) = 608

A minimal faithful permutation representation — 2 generators on 51 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1389, C₁₉×#12646, C₁₉×#12649, …
maximal normal subgroup of	C₂×C₁₉×#1389, C₁₉×#12646, C₁₉×#12649, …
maximal quotient of	C₁₉×#7159, C₁₉×#7175, C₁₉×#7177, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 121);