C₁₉×#7484 #18013443

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7481
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7484

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1390
commutator	C₂×Q₈	C₄²×C₁₉
Frattini, cosocle	#532	C₂²×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₂×Q₈ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#532 ◁ G

266 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 66 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 2 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,28,25,31,40,47)(22,32,34,26,37,42,50,44)(24,30,38,27,41,29,39,45)(33,48,36,46,51,43,35,49);(20,22,24,35,25,37,41,36)(21,26,29,43,31,44,30,48)(23,33,38,50,40,51,39,34)(27,32,28,46,45,42,47,49)

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 472);