C₁₉×#13437 #18019396

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13436
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13437

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2044
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₉
prime radical	C₁₉×#535	C₂²
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

422 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 86 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)(20,21,26,31)(22,32,36,49)(23,27,25,29)(24,38,39,30)(28,43,45,35)(33,47,34,48)(37,46,40,42)(41,50,44,51);(21,27)(22,33)(23,25)(24,39)(29,31)(30,46)(34,36)(35,50)(38,42)(41,44)(43,51)(47,48);(20,22,23,34,26,36,25,33)(21,28,29,44,31,45,27,41)(24,35,37,51,39,43,40,50)(30,32,46,47,38,49,42,48)

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6425);