C₁₉×#7446 #18013405

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7418
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7446

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#357
commutator	C₂×C₁₆	C₂×C₄×C₁₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₉
prime radical	C₂×C₁₉×D₁₆	C₄
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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)(20,21,22,25,23,24,26,27)(29,35,36,51)(30,40)(31,46)(32,42)(33,48)(37,54,38,55)(39,56,50,53)(41,47,52,49)(43,45)(44,59)(57,58);(21,24)(22,26)(28,29)(30,41)(31,47)(32,49)(33,50)(34,36)(35,43)(37,46)(38,42)(39,48)(40,51)(44,54)(45,52)(53,58)(55,57)(56,59)

Conjugacy classes & character table

931 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 434);