C₁₉×#12300 #18018259

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12298
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12300

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1613
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
prime radical	C₁₉×#3197	C₂
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ G

328 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 70 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)(20,21,25,40,26,30,23,28)(22,31,32,45,34,49,41,48)(24,36,39,29,38,46,35,47)(27,37,42,33,44,50,43,51);(20,22)(21,27)(23,32)(24,37)(25,41)(26,34)(28,42)(29,45)(30,44)(31,46)(33,35)(36,49)(38,50)(39,51)(40,43)(47,48);(20,23,26,25)(21,28,30,40)(22,32,34,41)(24,35,38,39)(27,42,44,43)(29,46,47,36)(31,48,49,45)(33,50,51,37)

Conjugacy classes & character table

475 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5288);