C₁₉×#1437 #14559294

order	2432
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₉ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₁₉×#1437

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂³
commutator	C₂²	C₂×C₄²×C₁₉
Frattini, cosocle	C₂⁴	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

828 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 828 conjugacy classes of subgroups — too many to draw. Only its 280 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)(21,23)(24,25,27,26)(29,30)(32,33,35,34);(28,29,31,30)(32,33,35,34);(20,21,22,23)(24,26,27,25)(28,30,31,29)(32,34,35,33)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₉×#7213, C₁₉×#8346, C₂×C₁₉×#1437, …
maximal normal subgroup of	C₁₉×#7213, C₁₉×#8346, C₂×C₁₉×#1437, …
maximal quotient of	C₁₉×#7554, C₁₉×#7555, C₁₉×#7556, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 169);