C₁₉×#11991 #18017950

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11989
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#11991

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1551
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#540	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#405 ◁ G

280 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 98 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)(20,21,23,29,36,26,35,39,25,30,38,45,24,28,37,44)(22,31,33,46,48,42,49,50,32,43,47,51,34,27,40,41);(21,26)(23,35)(24,36)(27,31)(28,30)(29,45)(33,49)(34,48)(37,38)(40,47)(41,50)(42,43);(20,22)(21,27,30,42)(23,33)(24,34)(25,32)(26,31,28,43)(29,41,45,50)(35,49)(36,48)(37,40)(38,47)(39,46,44,51)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4979);