C₁₉×#33728 #18039687

order	4864
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#33728

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×D₈
prime radical	C₂³×C₁₉	C₂×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

482 conjugacy classes of subgroups; only the 270 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 270 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) = 59
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 4 generators on 59 points:

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

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, 26716);