C₁₉×#1929 #14559786

order	2432
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#1929

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	C₄×D₄
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

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

normal subgroups only

This group has 224 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 — 3 generators on 39 points:

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

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1929, C₁₉×#21070, C₁₉×#21071, …
maximal normal subgroup of	C₂×C₁₉×#1929, C₁₉×#21070, C₁₉×#21071, …
maximal quotient of	C₁₉×#9541, C₁₉×#9542, C₁₉×#9543, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 661);