C₁₉×#2734 #14560591

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#2734

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

456 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 224 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)(25,26)(29,30)(32,33,36,38)(34,35,39,37);(21,23)(24,25,28,26)(27,30,31,29)(32,34,36,39)(33,37,38,35);(20,21)(22,23)(24,26,28,25)(27,30,31,29);(24,27)(25,29)(26,30)(28,31)(32,35,36,37)(33,34,38,39)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7741, C₁₉×#7757, C₁₉×#7766, …
maximal normal subgroup of	C₁₉×#7741, C₁₉×#7757, C₁₉×#7766, …
maximal quotient of	C₁₉×#14406, C₁₉×#14441, C₁₉×#14450, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1466);