C₁₉×#13660 #18019619

order	4864
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#13660

Subgroups

	subgroup	G/H
center	C₂×C₁₆×C₁₉	C₂³
commutator	C₂²	C₂²×C₁₆×C₁₉
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
socle, prime radical	C₂²×C₁₉	C₂²×C₁₆
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₁₆×C₁₉ ◁ G

158 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 59
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,27)(23,25)(24,26)(28,29,31,36,32,37,43,51,33,30,39,40,45,41,54,55,34,38,44,52,46,53,57,59,47,42,35,48,49,56,50,58);(20,22,24,23)(21,25,26,27);(20,23,24,22)(21,25,26,27)(28,30,31,40,32,41,43,55,33,38,39,52,45,53,54,59,34,42,44,48,46,56,57,58,47,29,35,36,49,37,50,51)

Conjugacy classes & character table

2128 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6648);