C₁₉×#1517 #14559374

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#1517

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₁₉×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

264 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 104 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) = 608

A minimal faithful permutation representation — 3 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)(23,25)(24,27)(28,29)(30,36,38,33)(31,34)(32,35)(37,42,39,41)(40,43);(21,25)(22,23)(26,27)(28,30)(29,33)(31,39)(32,38)(34,42)(35,36)(37,40)(41,43);(20,22,24,23)(21,25,27,26)(28,31,32,40)(29,34,35,43)(30,37,38,39)(33,41,36,42)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8428, C₁₉×#8429, C₁₉×#8430, …
maximal normal subgroup of	C₁₉×#8428, C₁₉×#8429, C₁₉×#8430, …
maximal quotient of	C₁₉×#7574, C₁₉×#7587, C₁₉×#7588, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 249);