C₁₉×#2168 #14560025

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×#2168

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

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

normal subgroups only

This group has 164 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)(24,25,27,31,28,26,33,34,29,32,36,39,37,35,30,38);(21,23);(24,26,27,34,28,32,33,39,29,35,36,38,37,25,30,31)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₁₉×#2168, C₁₉×#33432, C₁₉×#33433, …
maximal normal subgroup of	C₂×C₁₉×#2168, C₁₉×#33432, C₁₉×#33433, …
maximal quotient of	C₁₉×#12038, C₁₉×#12049, C₁₉×#12050, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 900);