C₁₉×#2189 #14560046

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#2189

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₂×C₁₉×#135	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

220 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 68 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 — 3 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)(24,25,30,34)(26,35,38,53)(27,32,29,44)(28,40,43,54)(31,46,49,37)(33,39,51,42)(36,52,45,50)(41,47,55,48);(24,26)(25,31)(27,36)(28,41)(29,45)(30,38)(32,47)(33,50)(34,49)(35,40)(37,42)(39,46)(43,55)(44,48)(51,52)(53,54);(21,23)(24,27,30,29)(25,32,34,44)(26,36,38,45)(28,39,43,42)(31,47,49,48)(33,40,51,54)(35,52,53,50)(37,41,46,55)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2189, C₁₉×#33516, C₁₉×#33519, …
maximal normal subgroup of	C₂×C₁₉×#2189, C₁₉×#33516, C₁₉×#33519, …
maximal quotient of	C₁₉×#12107, C₁₉×#12163, C₁₉×#12283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 921);