C₁₉×#1738 #14559595

order	2432
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#1738

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₄	C₂×C₄²×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₉	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

372 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 39
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#10744, C₁₉×#10753, C₁₉×#10767, …
maximal normal subgroup of	C₁₉×#10744, C₁₉×#10753, C₁₉×#10767, …
maximal quotient of	C₁₉×#7873, C₁₉×#7876, C₁₉×#7877, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 470);