C₁₉×#2129 #14559986

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2127
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#2129

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×#99
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×D₄	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

238 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

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

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12712, C₁₉×#12713, C₁₉×#12721, …
maximal normal subgroup of	C₁₉×#12712, C₁₉×#12713, C₁₉×#12721, …
maximal quotient of	C₁₉×#11434, C₁₉×#11449, C₁₉×#11482, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 861);