C₁₉×#7494 #18013453

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7493
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#7494

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1390
commutator	C₂×D₄	C₄²×C₁₉
Frattini, cosocle	#532	C₂²×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₂×D₄ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#532 ◁ G

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

normal subgroups only

This group has 270 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)(20,21,23,29)(22,32,34,46)(24,40,38,48)(25,30,42,28)(26,31,39,47)(27,36,43,50)(33,45,41,49)(35,51,37,44);(20,22,24,35,26,36,25,41)(21,27,30,44,31,46,40,45)(23,37,38,50,39,33,42,34)(28,43,47,51,48,32,29,49)

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, 482);