C₁₉×#7441 #18013400

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7440
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₉×#7441

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1353
commutator	C₂×M₁₆	C₂×C₄×C₁₉
Frattini, cosocle	#423	C₂²×C₁₉
prime radical	C₂³×C₁₉	#104
LCS	G ▷ C₂×M₁₆ ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#423 ◁ G

136 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 42 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)(22,30,32,42,34,47,33,50)(23,27,36,43)(24,38)(25,28)(26,31,40,48,41,49,46,35)(29,39)(37,45,51,44);(20,22)(21,26,28,41)(23,35,36,48)(24,33)(25,34)(27,42)(29,40,38,46)(30,45)(31,37,49,51)(32,39)(43,50)(44,47)

Conjugacy classes & character table

475 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 429);