C₁₉×#2234 #14560091

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₉×#2234

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₁₉×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

142 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 1216

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)(22,25)(23,24)(26,27)(29,33)(30,36)(32,39)(34,42)(35,38)(37,43)(40,41);(21,24)(25,27)(28,29,31,33)(30,34,37,41)(32,35,38,39)(36,40,43,42);(20,22,23,26)(21,25,24,27)(28,30,31,37)(29,34,33,41)(32,40,38,42)(35,43,39,36)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2234, C₁₉×#33645, C₁₉×#33647, …
maximal normal subgroup of	C₂×C₁₉×#2234, C₁₉×#33645, C₁₉×#33647, …
maximal quotient of	C₁₉×#12868, C₁₉×#12921, C₁₉×#12992, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 966);