C₁₉×#1586 #14559443

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

Aliases

direct product

C₁₉×#1586

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	C₄×D₄
prime radical	C₂×D₈×C₁₉	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

182 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 35
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1586, C₁₉×#17868, C₁₉×#17869, …
maximal normal subgroup of	C₂×C₁₉×#1586, C₁₉×#17868, C₁₉×#17869, …
maximal quotient of	C₁₉×#8204, C₁₉×#8212, C₁₉×#8288, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 318);