C₁₉×#2169 #14560026

order	2432
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#2169

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂³
commutator	C₂²	C₂²×C₈×C₁₉
Frattini, cosocle	C₂×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₂²×C₈
prime radical	C₂×D₄×C₁₉	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ G

162 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 100 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 — 3 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)(24,25,28,32,29,26,33,35,27,30,36,38,37,34,31,39);(21,23)(25,30)(26,34)(32,38)(35,39);(24,26,28,35,29,30,33,38,27,34,36,39,37,25,31,32)

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#7380, C₁₉×#12038, C₁₉×#12039, …
maximal normal subgroup of	C₁₉×#7380, C₁₉×#12038, C₁₉×#12039, …
maximal quotient of	C₁₉×#12039, C₁₉×#12051, C₁₉×#12054, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 901);