C₁₉×#2054 #14559911

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#2054

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂²×D₈×C₁₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

360 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 104 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) = 35
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(29,34)(30,35)(31,32);(24,25)(26,27)(28,29)(30,31)(32,34)(33,35);(21,23)(25,27)(28,30,31,29,33,34,32,35)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7080, C₁₉×#7088, C₁₉×#12158, …
maximal normal subgroup of	C₁₉×#7080, C₁₉×#7088, C₁₉×#12158, …
maximal quotient of	C₁₉×#10472, C₁₉×#10473, C₁₉×#10484, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 786);