C₁₉×#7650 #18013609

order	4864
nilpotency class	3
isoclinism	isoclinic class of #7606
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7650

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

384 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 130 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) = 59
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,25,24,26,22,27)(28,29)(30,36,38,33)(31,39)(32,35)(34,40)(37,41,43,42)(44,45)(46,52,54,59)(47,51)(48,50)(49,53,57,55)(56,58);(28,30,32,38)(29,33,35,36)(31,37,40,43)(34,41,39,42)(44,46)(45,49)(47,55)(48,54)(50,57)(51,59)(52,58)(53,56);(20,22,24,23)(21,25,26,27)(28,31,32,40)(29,34,35,39)(30,37,38,43)(33,41,36,42)(45,50)(49,57)(51,58)(52,59)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 638);