C₁₉×#2099 #14559956

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#2099

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

214 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 100 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)(20,21,24,26)(22,27,23,25)(28,29)(30,32)(31,33)(34,35);(20,22,24,23)(21,25,26,27)(28,30,31,34)(29,32,33,35)(36,37)(38,40)(39,42)(41,43);(20,23,24,22)(21,25,26,27)(29,33)(32,35)(37,40)(38,43)(41,42)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7787, C₁₉×#7788, C₁₉×#7791, …
maximal normal subgroup of	C₁₉×#7787, C₁₉×#7788, C₁₉×#7791, …
maximal quotient of	C₁₉×#10687, C₁₉×#11207, C₁₉×#11267, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 831);