C₁₉×#1820 #14559677

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#1820

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂³
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

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

normal subgroups only

This group has 300 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) = 43
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25)(23,24)(26,27)(28,29)(30,33)(31,38,39,34)(32,35)(36,42,43,40)(37,41);(21,24)(25,27)(28,30,32,37)(29,33,35,41)(31,36,39,43)(34,40,38,42);(20,22,23,26)(21,25,24,27)(28,31)(29,34)(30,36)(32,39)(33,40)(35,38)(37,43)(41,42)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7214, C₁₉×#7348, C₁₉×#8463, …
maximal normal subgroup of	C₁₉×#7214, C₁₉×#7348, C₁₉×#8463, …
maximal quotient of	C₁₉×#8699, C₁₉×#8701, C₁₉×#8703, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 552);