C₁₉×#7297 #18013256

order	4864
nilpotency class	4
isoclinism	isoclinic class of #1347
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7297

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	#102
commutator	C₂×C₈	C₄²×C₁₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₉
socle	C₂²×C₁₉	#340
prime radical	C₂³×C₁₉	#103
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

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

normal subgroups only

This group has 208 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 — 2 generators on 59 points:

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

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 285);