C₁₉×#1540 #14559397

order	2432
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#1540

Subgroups

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

256 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 108 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) = 1216

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

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8251, C₁₉×#8253, C₁₉×#8255, …
maximal normal subgroup of	C₁₉×#8251, C₁₉×#8253, C₁₉×#8255, …
maximal quotient of	C₁₉×#7560, C₁₉×#7565, C₁₉×#7642, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 272);