C₁₉×#2660 #14560517

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₉×#2660

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

448 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 232 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) = 2432

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)(24,25)(26,28)(27,29)(30,31)(32,33,36,34)(35,38,39,37);(20,21,22,23)(24,25,27,29)(26,28,31,30)(32,34,36,33)(35,37,39,38);(20,21)(22,23)(24,25)(26,30)(27,29)(28,31)(32,35,36,39)(33,37,34,38);(24,26,27,31)(25,28,29,30)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#10091, C₁₉×#10093, C₁₉×#10099, …
maximal normal subgroup of	C₁₉×#10091, C₁₉×#10093, C₁₉×#10099, …
maximal quotient of	C₁₉×#14276, C₁₉×#14277, C₁₉×#14282, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1392);