C₁₉×#18552 #18024511

order	4864
nilpotency class	3
isoclinism	isoclinic class of #18524
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#18552

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#555	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

982 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 230 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) = 1216

A minimal faithful permutation representation — 4 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)(22,29)(23,27)(24,32)(25,28)(26,30)(31,34)(33,35)(36,37,41,44)(38,46,49,50)(39,45,40,43)(42,48,51,47);(20,22,25,31)(21,26,28,35)(23,30,24,33)(27,34,32,29)(36,38,41,49)(37,42,44,51)(39,48,40,47)(43,50,45,46);(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29)(37,43)(39,40)(42,50)(44,45)(46,51)(47,48);(21,28)(26,35)(27,32)(29,34)(37,44)(42,51)(43,45)(46,50)

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 11540);