C₁₉×#1382 #14559239

order	2432
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1382

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	D₈
commutator	C₈	C₄²×C₁₉
Frattini, cosocle	C₂²×C₈	C₂²×C₁₉
socle	C₂²×C₁₉	#102
prime radical	C₂³×C₁₉	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

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

normal subgroups only

This group has 132 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) = 55
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 2 generators on 55 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)(26,35)(27,40)(28,43)(29,45)(30,34)(31,36)(32,42)(33,41)(37,47)(38,55)(39,51)(44,48)(46,54)(49,53)(50,52);(24,26,28,37,41,52,42,53,30,39,27,36,29,38,44,54)(25,31,32,35,45,49,43,55,34,47,48,51,33,46,40,50)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1382, C₁₉×#12561, C₄×C₁₉×#359, …
maximal normal subgroup of	C₂×C₁₉×#1382, C₁₉×#12561, C₄×C₁₉×#359, …
maximal quotient of	C₁₉×#7155, C₁₉×#7171, C₁₉×#7172, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 114);