C₁₉×#1521 #14559378

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#1521

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₁₉×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

218 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 88 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)(21,26,28,40)(22,31)(23,36)(27,42,43,48)(29,41,30,37)(32,47,44,39)(34,50)(35,46)(38,49)(45,51);(20,21)(22,32)(23,37)(24,29)(25,30)(26,38)(27,35)(28,33)(31,43)(34,47)(36,40)(39,50)(41,49)(42,51)(44,46)(45,48);(20,22,33,46)(21,27,28,43)(23,34,49,50)(24,35,25,31)(26,39,40,47)(29,32,30,44)(36,51,38,45)(37,42,41,48)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8500, C₁₉×#8501, C₁₉×#8502, …
maximal normal subgroup of	C₁₉×#8500, C₁₉×#8501, C₁₉×#8502, …
maximal quotient of	C₁₉×#7580, C₁₉×#7581, C₁₉×#7584, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 253);