C₁₉×#2186 #14560043

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#2186

Subgroups

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

230 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 68 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 — 3 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)(25,30)(26,29)(27,34)(31,39)(32,38)(33,36)(35,37);(24,25)(26,31)(27,35)(28,32)(29,37)(30,34)(33,38)(36,39);(21,23)(24,26,28,29)(25,31,32,37)(27,33,36,34)(30,35,38,39)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2186, C₁₉×#33516, C₁₉×#33519, …
maximal normal subgroup of	C₂×C₁₉×#2186, C₁₉×#33516, C₁₉×#33519, …
maximal quotient of	C₁₉×#12104, C₁₉×#12160, C₁₉×#12280, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 918);