C₁₉×#2243 #14560100

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2218
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₉×#2243

Subgroups

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

142 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 64 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)(28,29)(30,39)(31,36)(32,35)(33,41)(34,38)(37,40)(42,43);(21,24)(25,27)(28,29,32,36,33,37,39,43,34,38,42,30,40,41,31,35);(20,22,23,26)(21,25,24,27)(28,30,31,38,40,43,42,37,34,36,39,29,33,35,32,41)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12376, C₁₉×#12377, C₁₉×#12378, …
maximal normal subgroup of	C₁₉×#12376, C₁₉×#12377, C₁₉×#12378, …
maximal quotient of	C₁₉×#12890, C₁₉×#13149, C₁₉×#13150, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 975);