C₁₉×#18728 #18024687

order	4864
nilpotency class	3
isoclinism	isoclinic class of #18712
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#18728

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3548	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 920 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) = 2432

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

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, 11716);