C₁₉×#12429 #18018388

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12416
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12429

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#459
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#493	C₂²
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈²×C₁₉ ◁ G

240 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 82 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 — 3 generators on 59 points:

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

Conjugacy classes & character table

817 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5417);