C₁₉×#1914 #14559771

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1913
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#1914

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#386
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₁₉×#535	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

340 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 108 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)(20,21,24,28,25,27,34,22)(23,30,32,35,31,26,33,29);(20,22,24,27,25,28,34,21)(23,29,33,30,31,35,32,26);(20,23)(21,26)(22,29)(24,33)(25,31)(27,30)(28,35)(32,34)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12755, C₁₉×#12756, C₁₉×#12769, …
maximal normal subgroup of	C₁₉×#12755, C₁₉×#12756, C₁₉×#12769, …
maximal quotient of	C₁₉×#9107, C₁₉×#9109, C₁₉×#9187, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 646);