C₁₉×#3039 #14560896

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#3039

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

480 conjugacy classes of subgroups; only the 208 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 208 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) = 1216

A minimal faithful permutation representation — 4 generators on 39 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9171, C₁₉×#9172, C₁₉×#9316, …
maximal normal subgroup of	C₁₉×#9171, C₁₉×#9172, C₁₉×#9316, …
maximal quotient of	C₁₉×#19270, C₁₉×#19271, C₁₉×#19272, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1771);