C₁₉×#1827 #14559684

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1812
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#1827

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#117
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂×C₁₉	#381
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₁₉×#117 ◁ G

262 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 35
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,29,31,25)(23,28)(24,27)(26,30,33,35)(32,34);(20,22)(21,25)(23,30)(24,31)(26,28)(27,29)(32,35)(33,34);(20,22)(21,26,27,33)(23,30)(24,31)(25,28,29,34)(32,35)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12719, C₁₉×#12720, C₁₉×#12721, …
maximal normal subgroup of	C₁₉×#12719, C₁₉×#12720, C₁₉×#12721, …
maximal quotient of	C₁₉×#8730, C₁₉×#8731, C₁₉×#8732, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 559);