C₁₉×#13642 #18019601

order	4864
nilpotency class	3
isoclinism	isoclinic class of #1812
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#13642

Subgroups

	subgroup	G/H
center	C₈×C₁₉	#117
commutator	C₂×C₄	C₂²×C₈×C₁₉
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
socle	C₂×C₁₉	#2163
prime radical	C₂³×C₁₉	M₃₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ C₁₉×#346 ◁ G

170 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 106 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)(20,21,22,28,23,29,32,43,24,30,33,42,34,44,46,51,25,26,31,37,35,38,45,48,36,27,39,40,47,41,49,50);(21,26)(22,31)(27,30)(29,38)(32,45)(33,39)(41,44)(46,49);(21,27,26,30)(22,31)(28,42,37,40)(29,41,38,44)(32,45)(33,39)(43,51,48,50)(46,49)

Conjugacy classes & character table

1216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6630);