C₁₉×#3261 #14561118

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

Aliases

direct product

C₁₉×#3261

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#117 ◁ G

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

normal subgroups only

This group has 322 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) = 59
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,26)(28,29,33,37)(30,34,39,48)(31,41,43,51)(32,44,46,36)(35,45,50,42)(38,52,53,59)(40,56,55,49)(47,57,58,54);(20,21)(22,25)(23,24)(26,27)(28,30,33,39)(29,34,37,48)(31,38,43,53)(32,40,46,55)(35,47,50,58)(36,49,44,56)(41,52,51,59)(42,54,45,57);(21,24)(25,27)(28,31,33,43)(29,35,37,50)(30,38,39,53)(32,45,46,42)(34,47,48,58)(36,51,44,41)(40,57,55,54)(49,59,56,52);(20,22,23,26)(21,25,24,27)(30,39)(34,48)(38,53)(40,55)(47,58)(49,56)(52,59)(54,57)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12165, C₁₉×#12168, C₁₉×#12171, …
maximal normal subgroup of	C₁₉×#12165, C₁₉×#12168, C₁₉×#12171, …
maximal quotient of	C₁₉×#21898, C₁₉×#21968, C₁₉×#22124, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1993);