C₁₉×#1841 #14559698

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

Aliases

direct product

C₁₉×#1841

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#117
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂×C₁₉	#383
prime radical	C₂³×C₁₉	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ G

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

normal subgroups only

This group has 162 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) = 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)(22,30,33,34)(23,26)(24,28)(25,29)(27,32,35,31);(21,26,29,28)(27,34,35,30);(20,22,23,31,25,33,24,32)(21,27,28,30,29,35,26,34)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7225, C₁₉×#7226, C₁₉×#11836, …
maximal normal subgroup of	C₁₉×#7225, C₁₉×#7226, C₁₉×#11836, …
maximal quotient of	C₁₉×#8800, C₁₉×#8801, C₁₉×#8802, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 573);