C₁₉×#7134 #18013093

order	4864
nilpotency class	4
isoclinism	isoclinic class of #1366
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₉×#7134

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#333
commutator	C₄²	C₂×C₈×C₁₉
Frattini, cosocle	C₄³	C₂²×C₁₉
socle	C₂×C₁₉	#1272
prime radical	C₂³×C₁₉	#99
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₄³×C₁₉ ◁ G

230 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 304

A minimal faithful permutation representation — 2 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)(22,29,31,25,30,34,32,35)(23,26)(24,28)(27,33);(20,22,24,30)(21,25)(23,32,33,31)(26,29)(27,34)(28,35)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 122);