C₁₉×#8734 #18014693

order	4864
nilpotency class	3
isoclinism	isoclinic class of #1828
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#8734

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#381
commutator	C₂³	C₂²×C₈×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

622 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 166 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) = 43
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 43 points:

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

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1722);