C₁₉×#12510 #18018469

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12503
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₁₉×#12510

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈²×C₁₉ ◁ G

262 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 4864

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)(23,31)(24,26)(25,29)(27,32)(30,34)(33,35)(36,37,44,38)(39,48,49,41)(40,45,51,50)(42,47,43,46);(20,22,23,29,24,30,32,35)(21,25,27,28,26,33,31,34)(36,38,48,45,42,47,40,49,44,37,41,50,43,46,51,39);(21,26)(25,33)(27,31)(28,34)(36,39,51,46,43,50,41,37,44,49,40,47,42,45,48,38)

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5498);