C₁₉×#2351 #14560208

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#2351

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

552 conjugacy classes of subgroups; only the 368 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 368 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) = 2432

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

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8766, C₁₉×#8767, C₁₉×#9176, …
maximal normal subgroup of	C₁₉×#8766, C₁₉×#8767, C₁₉×#9176, …
maximal quotient of	C₁₉×#13804, Q₈×C₁₉×#95, C₁₉×#13821, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1083);