C₁₉×#12527 #18018486

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

Aliases

direct product

C₁₉×#12527

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

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

normal subgroups only

This group has 306 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) = 43
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 43 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)(29,32)(30,38)(31,34)(35,40)(36,37)(39,42)(41,43);(20,21,22,24,23,25,26,27)(28,29,34,37,33,36,31,32)(30,39,42,38,41,35,40,43);(21,25)(24,27)(28,30,29,35,34,42,37,43,33,41,36,39,31,40,32,38)

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, 5515);