C₁₉×#1294 #14559151

order	2432
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#1294

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²⋊C₄
commutator	C₂×C₄	C₄²×C₁₉
Frattini, cosocle	C₂³×C₄	C₂²×C₁₉
prime radical	C₂⁴×C₁₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

276 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 96 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) = 608

A minimal faithful permutation representation — 2 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)(26,28)(27,30)(29,31)(32,33)(34,38)(35,37)(36,39);(25,28,30,29)(32,34)(33,36,37,38)(35,39)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1294, C₁₉×#8012, C₁₉×#8013, …
maximal normal subgroup of	C₂×C₁₉×#1294, C₁₉×#8012, C₁₉×#8013, …
maximal quotient of	C₁₉×#7025, C₁₉×#7028, C₁₉×#7029, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 26);