C₁₉×#2188 #14560045

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

Aliases

direct product

C₁₉×#2188

Subgroups

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

216 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 55
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25,29,33)(26,34,37,53)(27,38,42,52)(28,43,40,32)(30,45,47,35)(31,48,50,41)(36,54,44,49)(39,51,55,46);(24,26,29,37)(25,30,33,47)(27,39,42,55)(28,44,40,36)(31,49,50,54)(32,51,43,46)(34,52,53,38)(35,48,45,41);(21,23)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12106, C₁₉×#12107, C₁₉×#12112, …
maximal normal subgroup of	C₁₉×#12106, C₁₉×#12107, C₁₉×#12112, …
maximal quotient of	C₁₉×#12106, C₁₉×#12162, C₁₉×#12282, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 920);