C₁₉×#12117 #18018076

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12117
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#12117

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1595
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ G

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

normal subgroups only

This group has 424 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)(22,33)(23,27)(24,31)(25,30)(26,32)(28,35)(29,37)(34,46)(36,47)(38,43)(39,45)(40,42)(41,50)(44,51)(48,49);(21,27)(23,37)(24,25)(28,41)(29,31)(30,42)(32,43)(33,46)(34,49)(35,39)(38,40)(44,47)(45,48)(50,51);(20,22)(21,28)(23,34)(24,39)(25,35)(26,36)(27,41)(29,46)(30,47)(31,33)(32,45)(37,49)(38,51)(40,50)(42,44)(43,48)

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, 5105);