C₁₉×#1279 #14559136

order	2432
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#1279

Subgroups

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

208 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 120 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) = 2432

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)(25,29)(26,27)(30,31)(32,33,35,38,36,39,34,37);(21,23)(24,25,27,30,28,31,26,29)(33,37,39,38)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₁₉×#1279, C₁₉×#7890, C₁₉×#7891, …
maximal normal subgroup of	C₂×C₁₉×#1279, C₁₉×#7890, C₁₉×#7891, …
maximal quotient of	C₁₉×#7015, C₁₉×#7022, C₁₉×#7024, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 11);