C₁₉×#2369 #14560226

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₉×#2369

Subgroups

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

496 conjugacy classes of subgroups; only the 328 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 328 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)(20,21,23,22)(24,25,28,27)(26,30,31,29)(33,36)(37,38);(20,22,23,21)(25,27)(29,30)(32,33)(34,38)(35,36)(37,39);(24,26,28,31)(25,29,27,30);(24,27,28,25)(26,30,31,29)(32,34,35,39)(33,37,36,38)

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8927, C₁₉×#8928, C₁₉×#8929, …
maximal normal subgroup of	C₁₉×#8927, C₁₉×#8928, C₁₉×#8929, …
maximal quotient of	C₄⋊C₄²×C₁₉, C₁₉×#13818, C₁₉×#13826, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1101);