C₁₉×#3021 #14560878

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3019
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#3021

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

736 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 212 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 — 4 generators on 35 points:

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

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#13353, C₁₉×#13354, C₁₉×#13360, …
maximal normal subgroup of	C₁₉×#13353, C₁₉×#13354, C₁₉×#13360, …
maximal quotient of	C₁₉×#18135, C₁₉×#18141, C₁₉×#18145, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1753);