C₁₉×#1478 #14559335

order	2432
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#1478

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	C₂²×D₄×C₁₉	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 312 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) = 35
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 35 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)(28,29,30,32,31,33,34,35);(21,25)(22,23)(26,27);(20,22,24,23)(21,26,27,25)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8322, C₁₉×#8324, C₁₉×#8325, …
maximal normal subgroup of	C₁₉×#8322, C₁₉×#8324, C₁₉×#8325, …
maximal quotient of	C₁₉×#7572, C₁₉×#7576, C₁₉×#7580, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 210);