C₁₉×#7483 #18013442

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7481
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7483

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1390
commutator	C₂×Q₈	C₄²×C₁₉
Frattini, cosocle	C₂×C₄⋊Q₈	C₂²×C₁₉
prime radical	C₂³×C₁₉	#99
LCS	G ▷ C₂×Q₈ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×C₄⋊Q₈ ◁ G

262 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 66 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 — 2 generators on 51 points:

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

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, 471);