C₁₉×#12530 #18018489

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12525
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₁₉×#12530

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#493
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

284 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 94 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)(22,26)(25,27)(28,29,31,34)(30,38,40,52)(32,45,43,58)(33,46,44,37)(35,49,47,41)(36,51,48,39)(42,57,56,54)(50,55,53,59);(20,21,22,24,23,25,26,27)(29,34)(35,47)(36,48)(37,46)(38,52)(45,58)(50,53)(54,57);(21,25)(24,27)(28,30,39,55,33,42,43,49,31,40,51,59,44,56,32,41)(29,35,45,54,37,50,48,52,34,47,58,57,46,53,36,38)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5518);