C₁₉×#3259 #14561116

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3198
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#3259

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#117 ◁ G

370 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 168 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 — 4 generators on 43 points:

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

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12164, C₁₉×#12167, C₁₉×#12170, …
maximal normal subgroup of	C₁₉×#12164, C₁₉×#12167, C₁₉×#12170, …
maximal quotient of	C₁₉×#21897, C₁₉×#21968, C₁₉×#22126, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1991);