C₁₉×#1272 #14559129

order	2432
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1272

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₈×C₁₉
Frattini, cosocle	C₂×C₄²	C₂²×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

166 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 43
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 2 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26,27,24)(23,25)(29,32,33,34)(36,37,38,40,39,41,42,43);(20,22)(21,24)(23,27)(25,26)(28,29,31,33)(30,34,35,32)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7345, C₁₉×#7376, C₁₉×#7409, …
maximal normal subgroup of	C₁₉×#7345, C₁₉×#7376, C₁₉×#7409, …
maximal quotient of	C₁₉×#7025, C₁₉×#7128, C₁₉×#7129, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 4);