C₁₉×#2912 #14560769

order	2432
nilpotency class	3
isoclinism	isoclinic class of #576
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#2912

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator	C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

476 conjugacy classes of subgroups; only the 344 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 344 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) = 39
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(25,29)(27,34)(30,35)(31,36)(33,38)(37,39);(24,25,27,29,28,31,34,36)(26,30,33,35,32,37,38,39);(24,26)(25,30)(27,33)(28,32)(29,35)(31,37)(34,38)(36,39);(26,32)(30,37)(33,38)(35,39)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12873, C₁₉×#12874, C₁₉×#12934, …
maximal normal subgroup of	C₁₉×#12873, C₁₉×#12874, C₁₉×#12934, …
maximal quotient of	C₁₉×#17788, C₁₉×#17798, C₁₉×#17811, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1644);