C₁₉×#1772 #14559629

order	2432
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#1772

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉	D₄
commutator	C₄	C₂×C₄²×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	C₄×D₄
prime radical	C₂³×C₁₉	#41
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

232 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 152 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)(25,29,31,34)(30,36,37,38);(20,21,22,23)(24,25)(26,30)(27,34)(28,31)(29,35)(32,38)(33,37)(36,39);(24,26,27,32,28,33,35,39)(25,30,34,38,31,37,29,36)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₉×#7179, C₁₉×#7180, C₁₉×#7181, …
maximal normal subgroup of	C₁₉×#7179, C₁₉×#7180, C₁₉×#7181, …
maximal quotient of	C₁₉×#8266, C₁₉×#8267, C₁₉×#8270, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 504);