C₁₉×#13646 #18019605

order	4864
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#13646

Subgroups

	subgroup	G/H
center	C₂×C₁₆×C₁₉	C₂³
commutator	C₂²	C₂²×C₁₆×C₁₉
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
socle	C₂²×C₁₉	C₂²×C₁₆
prime radical	C₂×D₄×C₁₉	C₁₆
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₁₆×C₁₉ ◁ G

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

normal subgroups only

This group has 202 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) = 55
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 55 points:

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

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, 6634);