C₁₉×#13366 #18019325

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13366

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

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

normal subgroups only

This group has 382 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) = 63
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 3 generators on 63 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,27,29)(26,30,31,28)(32,33,35,38)(34,42,43,60)(36,48,46,61)(37,51,47,41)(39,55,53,44)(40,57,54,50)(45,62,52,58)(49,59,63,56);(20,21)(22,23)(24,26,27,31)(25,28,29,30)(33,38)(39,53)(40,54)(41,51)(42,60)(48,61)(56,59)(58,62);(21,23)(32,34,35,43)(33,39,38,53)(36,49,46,63)(37,52,47,45)(40,58,54,62)(41,59,51,56)(42,61,60,48)(44,57,55,50)

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, 6354);