C₁₉×#1997 #14559854

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#1997

Subgroups

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

260 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 120 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)(22,26)(23,24)(25,27)(28,29,31,34,32,33,35,30);(21,24)(25,26)(28,30,31,33,32,34,35,29);(20,22,23,27)(21,25,24,26)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8470, C₁₉×#8471, C₁₉×#8473, …
maximal normal subgroup of	C₁₉×#8470, C₁₉×#8471, C₁₉×#8473, …
maximal quotient of	C₁₉×#9878, C₁₉×#9879, C₁₉×#9882, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 729);