C₁₉×#13433 #18019392

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13432
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13433

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

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

normal subgroups only

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

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, 6421);