C₁₉×#12872 #18018831

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11663
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#12872

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ C₂³×C₈×C₁₉ ◁ G

398 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 1216

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)(20,21)(22,25)(23,24)(26,27)(28,29,32,37,33,39,47,38)(30,34,41,50,42,52,58,51)(31,43,45,36,46,35,44,53)(40,54,56,49,57,48,55,59);(21,24)(25,27)(28,30,33,42)(29,34,39,52)(31,40,46,57)(32,41,47,58)(35,48,43,54)(36,49,53,59)(37,50,38,51)(44,55,45,56);(20,22,23,26)(21,25,24,27)(29,35)(31,44)(32,47)(34,48)(36,37)(38,53)(39,43)(40,55)(41,58)(45,46)(49,50)(51,59)(52,54)(56,57)

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, 5860);