C₁₉×#12465 #18018424

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12465
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#12465

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1677
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#2213	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

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

normal subgroups only

This group has 196 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

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

Conjugacy classes & character table

589 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5453);