C₁₉×#1479 #14559336

order	2432
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#1479

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₄	C₂²×C₈×C₁₉
Frattini, cosocle	C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×C₁₉	C₂²⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

248 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 124 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)(20,21,22,24,23,25,26,27)(28,29)(30,37)(31,35)(32,41)(33,36)(34,39)(38,42)(40,43);(28,30,33,40)(29,34,36,42)(31,39,32,38)(35,43,41,37);(28,31,33,32)(29,35,36,41)(30,38,40,39)(34,37,42,43)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8323, C₁₉×#8324, C₁₉×#8325, …
maximal normal subgroup of	C₁₉×#8323, C₁₉×#8324, C₁₉×#8325, …
maximal quotient of	C₁₉×#7573, C₁₉×#7575, C₁₉×#7581, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 211);