C₁₉×#12518 #18018477

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12503
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂×C₈

Aliases

direct product

C₁₉×#12518

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#2246	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈²×C₁₉ ◁ G

330 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 110 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)(31,43)(32,35)(33,46)(34,40)(36,39)(37,44)(41,50)(42,57)(45,58)(47,56)(48,59)(49,54)(51,53)(52,55);(28,30,39,53,33,42,45,56,32,41,54,59,44,55,31,40)(29,34,43,52,37,48,49,50,35,47,58,57,46,51,36,38);(20,21,25,27,23,26,22,24)(29,35)(34,47)(36,49)(37,46)(38,50)(43,58)(48,51)(52,57)

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5506);