C₁₉×#1828 #14559685

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1828
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#1828

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#381
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂⁴×C₁₉ ◁ G

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

normal subgroups only

This group has 296 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)(22,28,30,25)(23,31)(24,27)(26,32)(29,33,35,34);(20,22)(21,25)(23,29)(24,30)(26,33)(27,28)(31,34)(32,35);(20,23)(21,26,27,31)(22,29)(24,32)(25,33,28,34)(30,35)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12725, C₁₉×#12726, C₁₉×#12727, …
maximal normal subgroup of	C₁₉×#12725, C₁₉×#12726, C₁₉×#12727, …
maximal quotient of	C₁₉×#8734, C₁₉×#8735, C₁₉×#8736, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 560);