C₁₉×#2225 #14560082

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#2225

Subgroups

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

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

normal subgroups only

This group has 130 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) = 43
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,25)(22,26,27,24)(29,33)(30,36)(31,38)(34,43)(35,42)(37,40)(39,41);(20,22,23,27)(21,24,25,26);(28,29,32,35)(30,37,39,43)(31,40,38,34)(33,41,42,36)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12369, C₁₉×#12370, C₁₉×#12377, …
maximal normal subgroup of	C₁₉×#12369, C₁₉×#12370, C₁₉×#12377, …
maximal quotient of	C₁₉×#12812, C₁₉×#12938, C₁₉×#13110, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 957);