C₁₉×#12311 #18018270

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12310
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#12311

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1619
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

366 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 78 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)(22,30)(23,34)(24,37)(26,40)(27,35)(28,39)(31,36)(32,48)(33,47)(38,44)(41,45)(42,51)(43,50)(46,49);(20,21,25,29)(22,26,32,42)(23,35,38,49)(24,39,37,28)(27,44,46,34)(30,45,48,50)(31,43,33,41)(36,40,47,51);(20,22)(21,26)(23,36)(24,31)(25,32)(27,45)(28,41)(29,42)(30,34)(33,37)(35,40)(38,47)(39,43)(44,48)(46,50)(49,51)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5299);