C₁₉×#3059 #14560916

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3057
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#3059

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

460 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 55
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 55 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#11869, C₁₉×#11871, C₁₉×#13075, …
maximal normal subgroup of	C₁₉×#11869, C₁₉×#11871, C₁₉×#13075, …
maximal quotient of	C₁₉×#19188, C₁₉×#19193, C₁₉×#19199, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1791);